A101917 G.f. satisfies: A(x) = 1/(1 + x*A(x^7)) and also the continued fraction: 1 + x*A(x^8) = [1; 1/x, 1/x^7, 1/x^49, 1/x^343, ..., 1/x^(7^(n-1)), ...].

1, -1, 1, -1, 1, -1, 1, -1, 2, -3, 4, -5, 6, -7, 8, -10, 13, -17, 22, -28, 35, -43, 53, -66, 83, -105, 133, -168, 211, -264, 330, -413, 518, -651, 819, -1030, 1294, -1624, 2037, -2555, 3206, -4025, 5055, -6349, 7973, -10010, 12565, -15771, 19796, -24851, 31200, -39173, 49183, -61748, 77519, -97315, 122166

Offset

0,9

Links

Table of n, a(n) for n=0..56.

Formula

This was conjectured to have g.f. (1+x^7) / (1+x+x^7) by Ralf Stephan, May 17 2007, but this is wrong. This g.f. produces a sequence which differs at a(57) = -153367. The g.f. gives a(57) = -153366. - Johannes W. Meijer, Aug 08 2011

a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/7)} a(k) * a(n-7*k-1). - Ilya Gutkovskiy, Mar 01 2022

Maple

nmax:=57: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(A101917(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^7)), x, k+1); for n from 0 to k do x(n):=coeff(f(x), x, n) od: A101917(k):=x(k): od: seq(A101917(n), n=0..nmax); # Johannes W. Meijer, Aug 08 2011

Mathematica

m = 57; A[_] = 0; Do[A[x_] = 1/(1 + x A[x^7]) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)

Prog

(PARI) a(n)=local(A); A=1-x; for(i=1, n\7+1, A=1/(1+x*subst(A, x, x^7)+x*O(x^n))); polcoeff(A, n, x)
(PARI) a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(7))+1, n, 1/x^(7^(n-1)))))); polcoeff(M[1, 1]/M[2, 1]+x*O(x^(8*n+1)), 8*n+1)

Crossrefs

Cf. A101912, A101913, A101914, A101915, A101916, A101918.

Sequence in context: A236310 A005709 A017901 * A322854 A322802 A322799

Adjacent sequences: A101914 A101915 A101916 * A101918 A101919 A101920

Keyword

sign

Author

Paul D. Hanna, Dec 20 2004

Status

approved