A132824 Row sums of triangle A132823.
1, 2, 2, 4, 10, 24, 54, 116, 242, 496, 1006, 2028, 4074, 8168, 16358, 32740, 65506, 131040, 262110, 524252, 1048538, 2097112, 4194262, 8388564, 16777170, 33554384, 67108814, 134217676, 268435402, 536870856, 1073741766, 2147483588, 4294967234, 8589934528
Offset: 0
Examples
a(4) = 10 = sum of row 4 terms of triangle A132823: (1 + 2 + 4 + 2 + 1). a(3) = 4 = (1, 3, 3, 1) dot (1, 1, -1, 3) = (1 + 3 -3 + 3).
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
Programs
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Maple
A132824:=n->`if`(n=0, 1, 2+2^n-2*n); seq(A132824(n), n=0..30); # Wesley Ivan Hurt, Jun 06 2014
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Mathematica
a[0] = 1; a[n_] := 2 + 2^n - 2*n; Table[a[n], {n, 0, 30}] (* Wesley Ivan Hurt, Jun 06 2014 *)
Formula
Binomial transform of [1, 1, -1, 3, -1, 3, -1, 3, -1, 3, ...].
For n > 0, a(n) = 2 + 2^n - 2*n = 1 + A183155(n-1). - R. J. Mathar, Apr 04 2012
From Colin Barker, Jun 06 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.
G.f.: -(4*x^3-x^2-2*x+1)/((x-1)^2*(2*x-1)). (End)
For n > 1, a(n) = A132732(n-1). - Jeppe Stig Nielsen, Dec 29 2017
From Elmo R. Oliveira, Apr 03 2025: (Start)
E.g.f.: exp(x)*(exp(x) - 2*(x - 1)) - 2.
a(n) = 2*A000325(n-1) for n >= 1. (End)