User:Jason Kimberley/A068934

A068934

Triangular array C(n,r) that counts the isomorphism classes of connected r-regular simple graphs on n vertices.

For $r>3$, these are the output from Markus Meringer's GENREG. The italicised values are from Jason Kimberley running GENREG at The University of Newcastle High Performance Computing Facility for the durations described in the column sequences.

girth	C	D	E
$\geq$	Cge	Dge	Ege
$=$	Ceq	Deq	Eeq

C D E

Girth at least: 3 4 5 6 7 8

A005177	$n$			A179184	A002851	A006820	A006821	A006822	A014377	A014378	A014381	A014382	A014384
$\forall$	$r$	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39
1	1	1
1	2	0	1
1	3	0	0	1
2	4	0	0	1	1
2	5	0	0	1	0	1
5	6	0	0	1	2	1	1
4	7	0	0	1	0	2	0	1
17	8	0	0	1	5	6	3	1	1
22	9	0	0	1	0	16	0	4	0	1
167	10	0	0	1	19	59	60	21	5	1	1
539	11	0	0	1	0	265	0	266	0	6	0	1
18979	12	0	0	1	85	1544	7848	7849	1547	94	9	1	1
389436	13	0	0	1	0	10778	0	367860	0	10786	0	10	0	1
50314796	14	0	0	1	509	88168	3459383	21609300	21609301	3459386	88193	540	13	1	1
2942198440	15	0	0	1	0	805491	0	1470293675	0	1470293676	0	805579	0	17	0	1
1698517036411	16	0	0	1	4060	8037418	2585136675	113314233808	733351105934	733351105935	113314233813	2585136741	8037796	4207	21	1	1
	17	0	0	1	0	86221634	0	9799685588936	0		0	9799685588961	0	86223660	0	25	0	1
	18	0	0	1	41301	985870522	2807105250897							2807105258926	985883873	42110	33	1	1
	19	0	0	1	0	11946487647	0		0		0		0		0	11946592242	0	39	0	1
	20	0	0	1	510489	152808063181											152808993767	516344	49	1	1
	21	0	0	1	0	2056692014474	0		0		0		0		0		0	2056701139136	0	60	0	1
	22	0	0	1	7319447	not 28566273166527														7373924	73	1	1
	23	0	0	1	0		0		0		0		0		0		0		0		0	88	0	1
	24	0	0	1	117940535																	118573592	110	1	1
	25	0	0	1	0		0		0		0		0		0		0		0		0		0	130	0	1
	26	0	0	1	2094480864																			2103205738	158	1	1
	27	0	0	1	0		0		0		0		0		0		0		0		0		0		0	191	0	1
	28	0	0	1	40497138011																					40634185402	230	1	1
	29	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0	273	0	1
	30	0	0	1	845480228069																							847871397424	331	1	1
	31	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0		0	391	0	1
	32	0	0	1	18941522184590																									18987149095005	468	1	1
	33	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0		0		0	556	0	1
	34	0	0	1	453090162062723																											454032821688754	660	1	1
	35	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0		0		0		0	779	0	1
	36	0	0	1	11523392072541432																													11544329612485981	927	1	1
	37	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0		0		0		0		0	1087	0	1
	38	0	0	1	310467244165539782																															310964453836198311	1284	1	1
	39	0	0	1	0		0		0		0		0		0		0		0		0		0		0		0		0		0		0		0		0	1510	0	1
	40	0	0	1	8832736318937756165																																	8845303172513781271	1775	1	1