A296065 - OEIS

A296065

Partial sums of A296064.

0, 2, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 21, 0, 23, 0, 25, 0, 27, 0, 29, 0, 31, 0, 33, 0, 35, 0, 37, 0, 39, 0, 41, 0, 43, 0, 45, 0, 47, 0, 49, 0, 51, 0, 53, 0, 55, 0, 57, 0, 59, 0, 61, 0, 63, 0, 65, 0, 67, 0, 69, 0, 71, 0, 73, 0, 75

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OFFSET

1,2

COMMENTS

Essentially the same as A193356. - R. J. Mathar, Jan 02 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

G.f.: x^2*(2 + 3*x - 4*x^2 - x^3 + 2*x^4)/((1 - x)^2*(1 + x)^2). - Andrew Howroyd, Nov 08 2025

MATHEMATICA

Accumulate@ Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], IntegerQ@ Mean[Append[#, s k]]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {0}, 54] (* Michael De Vlieger, Dec 12 2017 *)

LinearRecurrence[{0, 2, 0, -1}, {0, 2, 3, 0, 5, 0}, 60] (* or *) Join[{0, 2}, Riffle[ 2*Range[ 30]+1, 0]] (* Harvey P. Dale, Oct 21 2021 *)

PROG

(PARI) a(n) = if(n==2 || (n > 2 && n%2), n, 0) \\ Andrew Howroyd, Nov 08 2025

CROSSREFS

Cf. A296064.

Sequence in context: A047814 A365276 A101991 * A174900 A344369 A175880

Adjacent sequences: A296062 A296063 A296064 * A296066 A296067 A296068

KEYWORD

nonn,easy

AUTHOR

Enrique Navarrete, Dec 04 2017

EXTENSIONS

More terms from Andrew Howroyd, Nov 08 2025

STATUS

approved