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A167625 Square array T(n,k), read by antidiagonals, counting isomorphism classes of k-regular multigraphs of order n, loops allowed. 1
1, 1, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 3, 2, 1, 1, 0, 5, 0, 3, 0, 1, 1, 7, 8, 7, 3, 1, 1, 0, 11, 0, 20, 0, 4, 0, 1, 1, 15, 31, 56, 32, 13, 4, 1, 1, 0, 22, 0, 187, 0, 66, 0, 5, 0, 1, 1, 30, 140, 654, 727, 384, 101, 22, 5, 1, 1, 0, 42, 0, 2705, 0, 3369, 0, 181, 0, 6, 0, 1, 1, 56, 722, 12587, 42703 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

The number of vertices n is positive; valency k is nonnegative.

Each loop contributes two to the valency of its vertex.

The antidiagonal having coordinate sum t=n+k is read from T(t,0) to T(1,t-1).

LINKS

J. S. Kimberley, Antidiagonals of T(n,k) for n+k in 1..19.

J. S. Kimberley, Table in user subpage of wiki.

R. C. Read, The enumeration of locally restricted graphs (I), J. London Math. Soc. 34 (1959) 417-436.

FORMULA

T(n,k) = N\{S_n[S_k] * S_{nk/2}[S_2]\}.

CROSSREFS

Column sequences: A000012 (k=0), A059841 (k=1), A41 (k=2), A129427 (k=3), A129429 (k=4), A129431 (k=5), A129433 (k=6), A129435 (k=7), A129437 (k=8).

Sequence in context: A058725 A068446 A253830 * A107261 A265336 A219782

Adjacent sequences:  A167622 A167623 A167624 * A167626 A167627 A167628

KEYWORD

nonn,tabl

AUTHOR

Jason Kimberley, Nov 07 2009

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)