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 A110023 A triangle of coefficients based on A000931 and Pascal's triangle: a(n)=a(n-2)+a(n-3); t(n,m)=a(n - m + 1)*a(m + 1)*Binomial[n, m]. 0
 1, 1, 1, 2, 2, 2, 2, 6, 6, 2, 3, 8, 24, 8, 3, 4, 15, 40, 40, 15, 4, 5, 24, 90, 80, 90, 24, 5, 7, 35, 168, 210, 210, 168, 35, 7, 9, 56, 280, 448, 630, 448, 280, 56, 9, 12, 81, 504, 840, 1512, 1512, 840, 504, 81, 12, 16, 120, 810, 1680, 3150, 4032, 3150, 1680, 810, 120, 16 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are: {1, 2, 6, 16, 46, 118, 318, 840, 2216, 5898, 15584} LINKS FORMULA a(n)=a(n-2)+a(n-3); t(n,m)=a(n - m + 1)*a(m + 1)*Binomial[n, m]. EXAMPLE {1}, {1, 1}, {2, 2, 2}, {2, 6, 6, 2}, {3, 8, 24, 8, 3}, {4, 15, 40, 40, 15, 4}, {5, 24, 90, 80, 90, 24, 5}, {7, 35, 168, 210, 210, 168, 35, 7}, {9, 56, 280, 448, 630, 448, 280, 56, 9}, {12, 81, 504, 840, 1512, 1512, 840, 504, 81, 12}, {16, 120, 810, 1680, 3150, 4032, 3150, 1680, 810, 120, 16} MATHEMATICA Clear[t, a, n, m] a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; t[n_, m_] := a[(n - m + 1)]*a[(m + 1)]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}] Flatten[%] CROSSREFS Cf. A141611, A141617, A000931. Sequence in context: A075094 A238413 A151704 * A279466 A116863 A136494 Adjacent sequences:  A110020 A110021 A110022 * A110024 A110025 A110026 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Aug 24 2008 STATUS approved

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Last modified May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)