A213758 Antidiagonal sums of the convolution array A213756.
1, 9, 40, 130, 355, 871, 1994, 4360, 9245, 19205, 39356, 79934, 161415, 324755, 651870, 1306596, 2616609, 5237265, 10479280, 20964090, 41934571, 83876479, 167761330, 335532160, 671075045, 1342162141, 2684337764, 5368690550
Offset: 1
Links
- Clark Kimberling, Table of n, a(n) for n = 1..100
- Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).
Programs
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Mathematica
(See A213756.)
Formula
a(n) = (1/6)*(-120 + 15*2^(n+3) - 81*n - 21*n^2 - 4*n^3).
a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).
G.f.: f(x)/g(x), where f(x) = x*(1 + 3*x) and g(x) = (1 - 2*x)*(1 - x)^4.