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A117403 a(n) = Sum_{k=0..[n/2]} 2^((n-2*k)*k) for n>=0. 2
1, 1, 2, 3, 6, 13, 34, 105, 386, 1681, 8706, 53793, 395266, 3442753, 35659778, 440672385, 6476038146, 112812130561, 2336999211010, 57759810847233, 1697654543745026, 59146046307566593, 2450521284684021762 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals the antidiagonal sums of triangle A117401.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: A(x) = Sum_{n>=0} x^n / (1 - 2^n*x^2).

a(2*n) = Sum_{k=0..n} 4^((n-k)*k);

a(2*n+1) = Sum_{k=0..n} 2^k * 4^((n-k)*k).

G.f.: 1/(1-x^2) - x/(Q(0) +x-x^3), where Q(k) = x^2*(2+x)*2^k -1-x - x*(2*x^2*2^k -1)^2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 11 2013

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 13*x^5 + 34*x^6 + 105*x^7 +...

where

A(x) = 1/(1-x^2) + x/(1-2*x^2) + x^2/(1-4*x^2) + x^3/(1-8*x^2) + x^4/(1-16*x^2) + ...

PROG

(PARI) a(n)=sum(k=0, n\2, 2^((n-2*k)*k))

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/(1-2^m*x^2 +x*O(x^n))), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A117401 (triangle), A117402 (row sums).

Sequence in context: A202086 A227366 A171878 * A002877 A065845 A137273

Adjacent sequences:  A117400 A117401 A117402 * A117404 A117405 A117406

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 12 2006

EXTENSIONS

Name changed by Paul D. Hanna, Nov 11 2013

STATUS

approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)