A210825 G.f.: Sum_{n>=1} a(n)*x^n/(1-x^n) = x*Sum_{n>=1} x^(n*(n-1)/2).

1, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, -1, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1, -1, 0, 1, -1, -1, -1, 0, 1, 0, -1, 0, 0, 2, 1, -1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1

Offset

1,56

Links

Paul D. Hanna, Table of n, a(n) for n = 1..1035

Example

G.f.: x/(1-x) - x^3/(1-x^3) - x^5/(1-x^5) - x^8/(1-x^8) - x^13/(1-x^13) - x^14/(1-x^14) + x^15/(1-x^15) + x^16/(1-x^16) - x^17/(1-x^17) +...+ a(n)*x^n/(1-x^n) +...
= x + x^2 + x^4 + x^7 + x^11 + x^16 + x^22 + x^29 +...+ x^(n*(n-1)/2+1) +...

Prog

(PARI) {a(n)=local(TRI=sum(k=1, sqrtint(4*n+1), x^(k*(k-1)/2))); if(n==1, 1, polcoeff(x*TRI-sum(m=1, n-1, a(m)*x^m/(1-x^m+x*O(x^n))), n))}
for(n=1, 30, print1(a(n), ", "))
(PARI) /* Vectorized form (faster): */
{A=[1]; for(i=1, 256, print1(A[#A], ", "); A=concat(A, 0); A[#A]=polcoeff(x*sum(k=1, sqrtint(2*#A)+1, x^(k*(k-1)/2)) - sum(m=1, #A-1, A[m]*x^m/(1-x^m+x*O(x^#A))), #A)); print1(A[#A])}
{sum(n=1, #A, A[n]*x^n/(1-x^n+O(x^(#A))))} /* Verify Lambert series */

Crossrefs

Cf. A008836.

Sequence in context: A334568 A072617 A348541 * A056226 A044935 A321920

Adjacent sequences: A210822 A210823 A210824 * A210826 A210827 A210828

Keyword

sign

Author

Paul D. Hanna, Mar 27 2012

Status

approved