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A117572 Expansion of (1+2x^2)/((1-x^2)(1-x^3)). 2
1, 0, 3, 1, 3, 3, 4, 3, 6, 4, 6, 6, 7, 6, 9, 7, 9, 9, 10, 9, 12, 10, 12, 12, 13, 12, 15, 13, 15, 15, 16, 15, 18, 16, 18, 18, 19, 18, 21, 19, 21, 21, 22, 21, 24, 22, 24, 24, 25, 24, 27, 25, 27, 27, 28, 27, 30, 28, 30, 30, 31, 30, 33, 31, 33, 33, 34, 33, 36, 34, 36, 36, 37, 36, 39, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Diagonal sums of A110128 [this cross-reference is wrong - N. J. A. Sloane, Jan 01 2008]. Partial sums are A117573.

LINKS

Table of n, a(n) for n=0..75.

FORMULA

a(n)=a(n-2)+a(n-3)-a(n-5); a(n)=cos(2*pi*n/3+pi/3)/3-sin(2*pi*n/3+pi/3)/sqrt(3)+3(-1)^n/4+(6n+7)/12; a(n)=sum{k=0..floor(n/2),2*A001045(L((n-2k+2)/3))} where L(j/p) is the Legendre symbol of j and p.

PROG

(Maxima) a(n):=(n+1)/2+3/4*(-1)^n+1/12-(1/3)*(-2)^fix(mod(n, 3)/2); Tani Akinari, Nov 10 2012

CROSSREFS

Sequence in context: A244965 A049996 A143908 * A029153 A060241 A145015

Adjacent sequences:  A117569 A117570 A117571 * A117573 A117574 A117575

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 29 2006

STATUS

approved

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Last modified March 26 00:20 EDT 2019. Contains 321478 sequences. (Running on oeis4.)