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

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

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)

Example

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).

Maple

A132824:=n->`if`(n=0, 1, 2+2^n-2*n); seq(A132824(n), n=0..30); # Wesley Ivan Hurt, Jun 06 2014

Mathematica

a[0] = 1; a[n_] := 2 + 2^n - 2*n; Table[a[n], {n, 0, 30}] (* Wesley Ivan Hurt, Jun 06 2014 *)

Crossrefs

Cf. A000325, A132823, A183155.

Essentially the same as A132732.

Sequence in context: A100088 A217212 A025244 * A298898 A339830 A078801

Adjacent sequences: A132821 A132822 A132823 * A132825 A132826 A132827

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 02 2007

Status

approved