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 A136564 Array read by rows: T(n,k) is the number of directed multigraphs with loops with n arcs, k vertices, and no vertex of degree 0. 7
 1, 1, 1, 5, 4, 1, 1, 9, 21, 16, 4, 1, 1, 18, 71, 108, 71, 22, 4, 1, 1, 27, 194, 491, 557, 326, 101, 22, 4, 1, 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1, 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1, 1, 84, 2095, 18823, 72064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Length of the n^th row: 2n. LINKS Table of n, a(n) for n=1..61. FORMULA T(n,1) = 1 if n > 0. T(n,2n) = 1 if n > 0. T(n,2n-1) = 4 if n >= 2. T(n,2n-k) = A144047(k) for n large enough (conjecturally, n >= 2k is enough). T(n,2) = (n^3 + 6*n^2 + 11*n - 6)/12 + ((n+2)/4)[n even]. (the bracket means that the second term is added if and only if n is even). - Benoit Jubin, Mar 31 2012 EXAMPLE 1, 1; 1, 5, 4, 1; 1, 9, 21, 16, 4, 1; 1, 18, 71, 108, 71, 22, 4, 1; 1, 27, 194, 491, 557, 326, 101, 22, 4, 1; 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1; 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1; CROSSREFS Row sums: A052171. Partial row sums: A138107. Sums of the first m entries of each row: A005993 (m=2), A050927 (m=3), A050929 (m=4). Sequence in context: A046575 A154739 A321044 * A136042 A268911 A351123 Adjacent sequences: A136561 A136562 A136563 * A136565 A136566 A136567 KEYWORD nonn,tabf AUTHOR Benoit Jubin, Apr 14 2008 EXTENSIONS More terms from Benoit Jubin and Vladeta Jovovic, Sep 08 2008 STATUS approved

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Last modified September 18 20:35 EDT 2024. Contains 376002 sequences. (Running on oeis4.)