A034299 Alternating sum transform (PSumSIGN) of A000975.

1, 1, 4, 6, 15, 27, 58, 112, 229, 453, 912, 1818, 3643, 7279, 14566, 29124, 58257, 116505, 233020, 466030, 932071, 1864131, 3728274, 7456536, 14913085, 29826157, 59652328, 119304642, 238609299

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			G.f. = 1 + x + 4*x^2 + 6*x^3 + 15*x^4 + 27*x^5 + 58*x^6 + 112*x^7 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2).

Crossrefs

Cf. A160156.

Programs

Magma

[(2^(n+5)+(6*n+13)*(-1)^n-9)/36: n in [0..50]]; // G. C. Greubel, Oct 12 2017

Mathematica

CoefficientList[Series[(1/(1-x^2))/(1-x-2x^2),{x,0,40}],x] (* Vincenzo Librandi, Apr 04 2012 *)
Table[(2^(n + 5) + (6 n + 13) (-1)^n - 9)/36, {n, 0, 28}] (* Bruno Berselli, Apr 04 2012 *)
LinearRecurrence[{1,3,-1,-2},{1,1,4,6},30] (* Harvey P. Dale, Jun 11 2019 *)

PARI

{a(n) = (32 * 2^n - 9 + (6*n + 13) * (-1)^n) / 36}; /* Michael Somos, Jan 23 2014 */

Formula

a(n) = sum{k=0..floor(n/2), A001045(n-2k+1)}. - Paul Barry, Nov 24 2003

G.f.: (1/(1-x^2))/(1-x-2x^2); a(n) = sum{k=0..n+1, A001045(k)*(1-(-1)^floor((n+k)/2))}; - Paul Barry, Apr 16 2005

a(n) = sum_{k, 0<=k<=n} A126258(n,k). - Philippe Deléham, Mar 13 2007

a(n) = 2*a(n-1)+A001057(n+1), with a(0)=1. - Bruno Berselli, Nov 09 2010

a(n) = (2^(n+5)+(6n+13)(-1)^n-9)/36. - Bruno Berselli, Apr 04 2012

a(n) = a(n-1) + 2*a(n-2) + (1 + (-1)^n) / 2. - Michael Somos, Jan 23 2014

A160156(n) = a(2*n). - Michael Somos, Oct 16 2020