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%I #6 Dec 02 2018 23:11:01
%S 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,
%T 35,168,210,210,168,35,7,9,56,280,448,630,448,280,56,9,12,81,504,840,
%U 1512,1512,840,504,81,12,16,120,810,1680,3150,4032,3150,1680,810,120,16
%N 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].
%C Row sums are:
%C {1, 2, 6, 16, 46, 118, 318, 840, 2216, 5898, 15584}
%F a(n)=a(n-2)+a(n-3); t(n,m)=a(n - m + 1)*a(m + 1)*Binomial[n, m].
%e {1},
%e {1, 1},
%e {2, 2, 2},
%e {2, 6, 6, 2},
%e {3, 8, 24, 8, 3},
%e {4, 15, 40, 40, 15, 4},
%e {5, 24, 90, 80, 90, 24, 5},
%e {7, 35, 168, 210, 210, 168, 35, 7},
%e {9, 56, 280, 448, 630, 448, 280, 56, 9},
%e {12, 81, 504, 840, 1512, 1512, 840, 504, 81, 12},
%e {16, 120, 810, 1680, 3150, 4032, 3150, 1680, 810, 120, 16}
%t 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[%]
%Y Cf. A141611, A141617, A000931.
%K nonn,tabl
%O 1,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 24 2008
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