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

0,7

Links

Table of n, a(n) for n=0..52.

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

Prog

(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)

Crossrefs

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

Sequence in context: A098131 A017899 A003520 * A295073 A322340 A282504

Adjacent sequences: A101912 A101913 A101914 * A101916 A101917 A101918

Keyword

sign

Author

Paul D. Hanna, Dec 20 2004

Status

approved