A101915 G.f. satisfies: A(x) = 1/(1 + x*A(x^5)) and also the continued fraction: 1+x*A(x^6) = [1;1/x,1/x^5,1/x^25,1/x^125,...,1/x^(5^(n-1)),...].

1, -1, 1, -1, 1, -1, 2, -3, 4, -5, 6, -8, 11, -15, 20, -26, 34, -45, 60, -80, 106, -140, 185, -245, 325, -431, 571, -756, 1001, -1326, 1757, -2329, 3086, -4088, 5415, -7173, 9504, -12593, 16685, -22105, 29284, -38796, 51400, -68100, 90225, -119535, 158365, -209810, 277970, -368275, 487916, -646421, 856416

Offset: 0

Author

Paul D. Hanna, Dec 20 2004

Keywords

• sign

Crossrefs

Cf. A101912, A101913, A101914, A101916, A101917, A101918.

Programs

PARI

a(n)=local(A);A=1-x;for(i=1,n\5+1, A=1/(1+x*subst(A,x,x^5)+x*O(x^n)));polcoeff(A,n,x)

PARI

a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(5))+1,n,1/x^(5^(n-1)))))); polcoeff(M[1,1]/M[2,1]+x*O(x^(6*n+1)),6*n+1)

Formula

a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/5)} a(k) * a(n-5*k-1). - Ilya Gutkovskiy, Mar 01 2022