A131093 a(1)=1, a(n) = a(n-1) + sum of odd numbers which are among the first (n-1) terms of the sequence.

1, 2, 3, 7, 18, 29, 69, 178, 287, 683, 1762, 2841, 6761, 17442, 28123, 66927, 172658, 278389, 662509, 1709138, 2755767, 6558163, 16918722, 27279281, 64919121, 167478082, 270037043, 642633047, 1657862098, 2673091149

Offset

1,2

Comments

a(n) mod 2 = A011655(n+1);

a(n) = a(n-1) + Sum(a(k)*(a(k) mod 2): 1<=k<n), a(1) = 1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Odd Number

Formula

Empirical g.f.: -x*(x-1)*(x^4+3*x^3+6*x^2+3*x+1) / (x^6-10*x^3+1). - Colin Barker, Mar 29 2013

Mathematica

nxt[{ot_, a_}]:=Module[{x=a+ot}, {If[OddQ[x], ot+x, ot], x}]; NestList[nxt, {1, 1}, 30][[All, 2]] (* Harvey P. Dale, Dec 18 2020 *)

Crossrefs

Cf. A096777, A101135.

Sequence in context: A225747 A058334 A303090 * A359089 A343358 A002864

Adjacent sequences: A131090 A131091 A131092 * A131094 A131095 A131096

Keyword

nonn

Author

Reinhard Zumkeller, Jun 14 2007

Status

approved