A223547 G.f.: A(x) = Sum_{n>=0} x^n / (1 - x^n - x^(2*n))^n.

1, 1, 2, 3, 6, 6, 17, 14, 36, 44, 81, 90, 225, 234, 456, 682, 1166, 1598, 2967, 4182, 7366, 11215, 18467, 28658, 48561, 75216, 123692, 197415, 322530, 514230, 841648, 1346270, 2191664, 3528178, 5723189, 9229251, 14975856, 24157818, 39147344, 63258564, 102444992, 165580142

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^n. - Vaclav Kotesovec, Nov 08 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 6*x^5 + 17*x^6 + 14*x^7 +...
where
A(x) = 1 + x/(1-x-x^2) + x^2/(1-x^2-x^4)^2 + x^3/(1-x^3-x^6)^3 + x^4/(1-x^4-x^8)^4 + x^5/(1-x^5-x^10)^5 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/(1-x^m-x^(2*m)+x*O(x^n))^m), n)}
for(n=0, 45, print1(a(n), ", "))

Crossrefs

Sequence in context: A102625 A117777 A371991 * A049297 A285664 A056391

Adjacent sequences: A223544 A223545 A223546 * A223548 A223549 A223550

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2013

Status

approved