A242634 G.f. A(x) satisfies A(x) = A(x^2) / (1 - x) + x / (1 - x^2).

0, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 13, 14, 18, 19, 24, 25, 31, 32, 40, 41, 50, 51, 63, 64, 77, 78, 95, 96, 114, 115, 138, 139, 163, 164, 194, 195, 226, 227, 266, 267, 307, 308, 357, 358, 408, 409, 471, 472, 535, 536, 612, 613, 690, 691, 785, 786, 881, 882

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Formula

G.f.: x / (1 - x) + Sum_{k>0} x^(3*2^(k-1)) / Product_{j=0..k} (1 - x^(2^j)).

a(n) = a(n-2) + a(floor(n/2)) unless n=1.

a(n) = A088585(n) - A088585(n-1) if n>=1.

a(n) = A088567(n) if n>0.

a(2*n + 1) = a(2*n) + 1 = A088585(n) if n>=0.

Example

G.f. = x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 6*x^8 + 7*x^9 + ...

Mathematica

a[ n_] := If[ n < 0, 0, Module[{A = 0}, Do[A = (x + (1 + x) (A /. x -> x^2)) / (1 - x^2), {IntegerLength[ n, 2]}]; SeriesCoefficient[ A, {x, 0, n}]]];

Prog

(PARI) {a(n) = my(A = O(x)); if( n<0, 0, for(k=1, #binary(n), A = (x + (1 + x) * subst(A, x, x^2)) / (1 - x^2)); polcoeff(A, n))};
(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, #binary(n\3), x^(2^k*3 \ 2) / prod(j=0, k, 1 - x^2^j), x * O(x^n)), n))};

Crossrefs

Cf. A088567, A088585.

Sequence in context: A133564 A342558 A017863 * A088567 A029014 A304631

Adjacent sequences: A242631 A242632 A242633 * A242635 A242636 A242637

Keyword

nonn

Author

Michael Somos, May 19 2014

Status

approved