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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 October 20 02:35 EDT 2019. Contains 328244 sequences. (Running on oeis4.)