A213843 Antidiagonal sums of the convolution array A213841.
1, 13, 62, 190, 455, 931, 1708, 2892, 4605, 6985, 10186, 14378, 19747, 26495, 34840, 45016, 57273, 71877, 89110, 109270, 132671, 159643, 190532, 225700, 265525, 310401, 360738, 416962, 479515, 548855, 625456, 709808, 802417, 903805, 1014510
Offset: 1
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A213841.
Programs
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Magma
[n*(1 + n)*(1 - 2*n + 4*n^2)/6 : n in [1..30]]; // Wesley Ivan Hurt, Oct 09 2014
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Maple
A213843:=n->n*(1 + n)*(1 - 2*n + 4*n^2)/6: seq(A213843(n), n=1..30); # Wesley Ivan Hurt, Oct 09 2014
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Mathematica
Table[n (1 + n) (1 - 2 n + 4 n^2)/6, {n, 30}] (* Wesley Ivan Hurt, Oct 09 2014 *)
Formula
a(n) = n*(1 + n)*(1 - 2*n + 4*n^2)/6.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: f(x)/g(x), where f(x) = x*(1 + x)(1 + 8*x) and g(x) = (1-x)^5.