



1, 2, 2, 2, 4, 4, 2, 4, 5, 4, 6, 4, 4, 8, 4, 4, 8, 6, 6, 8, 8, 4, 6, 8, 5, 12, 8, 4, 12, 8, 6, 8, 8, 8, 12, 10, 4, 12, 8, 8, 16, 8, 6, 12, 12, 8, 10, 8, 9, 14, 12, 8, 12, 16, 8, 16, 8, 4, 18, 8, 12, 16, 10, 8, 16, 16, 6, 16, 16, 8, 14, 12, 8, 20, 14, 12, 16, 8, 10, 16, 17, 8, 18, 16, 8, 20, 12
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..87.


FORMULA

a(4*n) = 2 * a(n). a(4*n + 1) = A045834(n). a(4*n + 2) = A005884(n).  Michael Somos, Jul 05 2015
G.f.: (Sum_{k>0} x^(k^2 + k  1) / (1  x^(2*k  1))^2) / (Sum_{k>0} x^(k*(k  1))).  Michael Somos, Jul 05 2015


EXAMPLE

G.f. = x + 2*x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 4*x^6 + 2*x^7 + 4*x^8 + 5*x^9 + ...


PROG

(PARI) {a(n) = my(A); if( n<1, 0, n; A = x * O(x^n); polcoeff( sum(k=1, sqrtint(4*n + 9)\2, x^(k^2 + k  2) / (1  x^(2*k  1))^2, A) / sum(k=1, sqrtint(4*n + 1)\2 + 1, x^(k^2  k), A), n))}; /* Michael Somos, Jul 05 2015 */


CROSSREFS

Cf. A005884, A045834.
Sequence in context: A105080 A336299 A206424 * A172309 A130453 A259981
Adjacent sequences: A117725 A117726 A117727 * A117729 A117730 A117731


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 14 2006


STATUS

approved



