A136169 a(n) = 2*a(n-1) - [(n+1)/3] for n>0 with a(0) = 1.

1, 2, 3, 5, 9, 16, 30, 58, 113, 223, 443, 882, 1760, 3516, 7027, 14049, 28093, 56180, 112354, 224702, 449397, 898787, 1797567, 3595126, 7190244, 14380480, 28760951, 57521893, 115043777, 230087544, 460175078, 920350146, 1840700281, 3681400551

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-3,2).

Formula

G.f.: (1 - x^2*(1+x+x^2)/(1-x^3)^2 )/(1-2*x).

Mathematica

nxt[{n_, a_}]:={n+1, 2a-Floor[(n+2)/3]}; NestList[nxt, {0, 1}, 50][[All, 2]] (* Harvey P. Dale, Aug 09 2021 *)

Prog

(PARI) {a(n)=if(n==0, 1, 2*a(n-1)-((n+1)\3))}

Crossrefs

Cf. A136219.

Sequence in context: A329700 A217282 A047061 * A047041 A352944 A154223

Adjacent sequences: A136166 A136167 A136168 * A136170 A136171 A136172

Keyword

nonn,easy

Author

Paul D. Hanna, Dec 23 2007

Status

approved