A101916 G.f. satisfies: A(x) = 1/(1 + x*A(x^6)) and also the continued fraction: 1+x*A(x^7) = [1;1/x,1/x^6,1/x^36,1/x^216,...,1/x^(6^(n-1)),...].

1, -1, 1, -1, 1, -1, 1, 0, -1, 2, -3, 4, -5, 5, -4, 2, 1, -5, 10, -15, 19, -21, 20, -15, 5, 10, -29, 50, -70, 85, -90, 80, -51, 1, 69, -154, 244, -324, 375, -376, 307, -153, -91, 414, -788, 1163, -1469, 1621, -1529, 1115, -328, -833, 2299, -3916, 5440, -6550, 6874, -6039, 3741, 170, -5600, 12135, -18990, 25008

Offset

0,10

Comments

This sequence resembles the series expansion of B(x) = (1+x^6)/(1+x+x^6). The first difference occurs at a(43) = 415 versus a(43) = 414. - Johannes W. Meijer, Aug 08 2011

Links

Table of n, a(n) for n=0..63.

Formula

a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/6)} a(k) * a(n-6*k-1). - Ilya Gutkovskiy, Mar 01 2022

Maple

nmax:=63: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(a(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^6)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: a(k):=x(k): od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Aug 08 2011

Prog

(PARI) a(n)=local(A); A=1-x; for(i=1, n\6+1, A=1/(1+x*subst(A, x, x^6)+x*O(x^n))); polcoeff(A, n, x)
(PARI) a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(6))+1, n, 1/x^(6^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(7*n+1)), 7*n+1)

Crossrefs

Cf. A101912-A101915, A101917-A101918.

Sequence in context: A335834 A289321 A301534 * A361979 A329267 A100771

Adjacent sequences: A101913 A101914 A101915 * A101917 A101918 A101919

Keyword

sign

Author

Paul D. Hanna, Dec 20 2004

Status

approved