A343561 2nd row of A341867: a(n) = (n^2+15*n+32)*2^(n-3).
4, 12, 33, 86, 216, 528, 1264, 2976, 6912, 15872, 36096, 81408, 182272, 405504, 897024, 1974272, 4325376, 9437184, 20512768, 44433408, 95944704, 206569472, 443547648, 950009856, 2030043136, 4328521728, 9210691584, 19562233856, 41473277952, 87778394112, 185488900096
Offset: 0
Links
- Jianing Song, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
Crossrefs
Cf. A341867.
Programs
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Mathematica
a[n_] := (n^2 + 15*n + 32)*2^(n - 3); Array[a, 31, 0] (* Amiram Eldar, Nov 08 2021 *)
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PARI
a(n) = (n^2+15*n+32)*2^(n-3)
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * (k^2+7*k+8)/2.
G.f.: (2 - 3*x)^2/(1 - 2*x)^3.
E.g.f.: exp(2*x) * (x^2/2 + 4*x + 4).