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A132824 Row sums of triangle A132823. 2
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 (list; graph; refs; listen; history; text; internal format)
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

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3) for n>3. - Colin Barker, Jun 06 2014

G.f.: -(4*x^3-x^2-2*x+1) / ((x-1)^2*(2*x-1)). - Colin Barker, Jun 06 2014

For n>1, a(n) = A132732(n-1). - Jeppe Stig Nielsen, Dec 29 2017

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. A132823, A183155, A132732.

Sequence in context: A100088 A217212 A025244 * A298898 A078801 A002420

Adjacent sequences:  A132821 A132822 A132823 * A132825 A132826 A132827

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Sep 02 2007

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)