n^2-n/2 - Page 7

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Carréphylic classes: n²-n/2 (for even n)

Here are the first 6 carréphylic numbers of the form n²-n/2 (for even n) with the usual data.
Root-3 is a 'small numbers exception' on the general pattern because it is also a member of n²-1 and shows the characteristic 'sp-block shift' of that class.
The first non-trivial ab-blocks (second for root-3) follow a simple pattern (4n-1)/4. The s/p- and t/q-fractions are the only ones above the root-value.
The values 'v' equal half the numerator of the first t/q fraction and the numerator of the first q/t fraction respectively.

√3

1	0	1	2	3	5	7	12	19	26	45	71	97	168	265	362	627	989	1351	2340	3691	5042	8733	13775	18817	32592	51409	70226	121635	191861	262087	453948	716035	978122	1694157	...
0	1	1	1	2	3	4	7	11	15	26	41	56	97	153	209	362	571	780	1351	2131	2911	5042	7953	10864	18817	29681	40545	70226	110771	151316	262087	413403	564719	978122	...

√14

1	0	1	2	3	4	7	11	15	56	71	86	101	116	217	333	449	1680	2129	2578	3027	3476	6503	9979	13455	50344	63799	77254	90709	104164	194873	299037	403201	1508640	1911841	2315042	2718243	3121444	5839687	8961131	12082575	45208856	...
0	1	1	1	1	1	2	3	4	15	19	23	27	31	58	89	120	449	569	689	809	929	1738	2667	3596	13455	17051	20647	24243	27839	52082	79921	107760	403201	510961	618721	726481	834241	1560722	2394963	3229204	12082575	...

√33

1	0	1	2	3	4	5	6	11	17	23	132	155	178	201	224	247	270	517	787	1057	6072	7129	8186	9243	10300	11357	12414	23771	36185	48599	279180	327779	376378	424977	473576	522175	570774	1092949	1663723	2234497	12836208	15070705	17305202	19539699	21774196	24008693	26243190	50251883	76495073	102738263	590186388	...
0	1	1	1	1	1	1	1	2	3	4	23	27	31	35	39	43	47	90	137	184	1057	1241	1425	1609	1793	1977	2161	4138	6299	8460	48599	57059	65519	73979	82439	90899	99359	190258	289617	388976	2234497	2623473	3012449	3401425	3790401	4179377	4568353	8747730	13316083	17884436	102738263	...

√60

1	0	1	2	3	4	5	6	7	8	15	23	31	240	271	302	333	364	395	426	457	488	945	1433	1921	14880	16801	18722	20643	22564	24485	26406	28327	30248	58575	88823	119071	922320	1041391	1160462	1279533	1398604	1517675	1636746	1755817	1874888	3630705	5505593	7380481	57168960	64549441	71929922	79310403	86690884	94071365	101451846	108832327	116212808	225045135	341257943	457470751	3543553200	...
0	1	1	1	1	1	1	1	1	1	2	3	4	31	35	39	43	47	51	55	59	63	122	185	248	1921	2169	2417	2665	2913	3161	3409	3657	3905	7562	11467	15372	119071	134443	149815	165187	180559	195931	211303	226675	242047	468659	710769	952816	7380481	8333297	9286113	10238929	11191745	12144561	13097377	14050193	15003009	29045391	44056211	59059220	457470751	...

√95

1	0	1	2	3	4	5	6	7	8	9	10	19	29	39	380	419	458	497	536	575	614	653	692	731	770	1501	2271	3041	29640	...
0	1	1	1	1	1	1	1	1	1	1	1	2	3	4	39	43	47	51	55	59	63	67	71	75	79	154	233	312	3041	...

√138

1	0	1	2	3	4	5	6	7	8	9	10	11	12	23	35	47	552	599	646	693	740	787	834	881	928	975	1022	1069	1116	2185	3301	4417	51888	...
0	1	1	1	1	1	1	1	1	1	1	1	1	1	2	3	4	47	51	55	59	63	67	71	75	79	83	87	91	95	186	281	376	4417	...

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Carréphylic classes - n^2-n/2

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