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A206739 G.f.: 1/(1 - x/(1 - x^4/(1 - x^9/(1 - x^16/(1 - x^25/(1 - x^36/(1 -...- x^(n^2)/(1 -...))))))), a continued fraction. 1
1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 37, 52, 72, 99, 138, 193, 269, 373, 518, 722, 1006, 1399, 1944, 2705, 3766, 5241, 7290, 10141, 14112, 19638, 27323, 38012, 52889, 73593, 102398, 142470, 198225, 275809, 383760, 533954, 742923, 1033685, 1438254 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..46.

FORMULA

G.f.: A(x)=-1/B(x), where B(x) is g.f. of A113047.  - Vladimir Kruchinin, Mar 21 2015

a(n) = sum(k=0..n, T(n,k)), where T(n, m)=sum(i=1..(n-m)/3, binomial(m, i)*T((n-m)/3,i)), T(n,n)=1. - Vladimir Kruchinin, Mar 21 2015

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 +...

PROG

(PARI) {a(n)=local(CF=1+x*O(x^n), M=sqrtint(n+1)); for(k=0, M, CF=1/(1-x^((M-k+1)^2)*CF)); polcoeff(CF, n, x)}

for(n=0, 55, print1(a(n), ", "))

(PARI) N = 66;  q = 'q + O('q^N);

G(k) = if(k>N, 1, 1 - q^((k+1)^2) / G(k+1) );

gf = 1 / G(0);

Vec(gf) \\ Joerg Arndt, Jul 06 2013

(Maxima)

T(n, m):=if n=m then 1 else  sum(binomial(m, i)*T((n-m)/3, i), i, 1, (n-m)/3);

makelist(sum(T(n, k), k, 0, n), n, 0, 20); /* Vladimir Kruchinin, Mar 21 2015 */

CROSSREFS

Cf. A206740.

Sequence in context: A017898 A003269 A087221 * A107586 A206737 A275174

Adjacent sequences:  A206736 A206737 A206738 * A206740 A206741 A206742

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 12 2012

STATUS

approved

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Last modified December 9 12:25 EST 2016. Contains 278971 sequences.