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

0,3

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).

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

Example

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

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 *)

Prog

(PARI) {a(n) = (32 * 2^n - 9 + (6*n + 13) * (-1)^n) / 36}; /* Michael Somos, Jan 23 2014 */
(Magma) [(2^(n+5)+(6n+13)(-1)^n-9)/36: n in [0..50]]; // G. C. Greubel, Oct 12 2017

Crossrefs

Cf. A160156.

Sequence in context: A045907 A254325 A351145 * A007135 A294070 A073603

Adjacent sequences: A034296 A034297 A034298 * A034300 A034301 A034302

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved