A132074 Row sums of triangle A132073.
1, 4, 9, 16, 27, 46, 81, 148, 279, 538, 1053, 2080, 4131, 8230, 16425, 32812, 65583, 131122, 262197, 524344, 1048635, 2097214, 4194369, 8388676, 16777287, 33554506, 67108941, 134217808, 268435539, 536870998, 1073741913, 2147483740
Offset: 0
Examples
a(4) = 27 = sum of row 4 terms of triangle A132073: (5 + 5 + 7 + 5 + 5). a(4) = 27 = (1, 4, 6, 4, 1) dot (1, 3, 2, 0, 2) = (1 + 12 + 12 + 0 + 2).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2). [From _R. J. Mathar_, May 21 2010]
Crossrefs
Cf. A132073.
Programs
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Magma
I:=[1, 4, 9, 16]; [n le 4 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 06 2012
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Mathematica
CoefficientList[Series[(2*x^2+2*x^3-1)/((2*x-1)*(x-1)^2),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
Formula
Binomial transform of [1, 3, 2, 0, 2, 0, 2, 0, 2, ...].
From R. J. Mathar, May 21 2010: (Start)
G.f.:= (2*x^2 + 2*x^3 - 1)/((2*x-1)*(x-1)^2).
a(n) = 2^n + 3*n - 1, n > 0. (End)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 06 2012
Extensions
More terms from R. J. Mathar, May 21 2010