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A077903
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Expansion of (1-x)^(-1)/(1+x-x^2+2*x^3).
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0
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1, 0, 2, -3, 6, -12, 25, -48, 98, -195, 390, -780, 1561, -3120, 6242, -12483, 24966, -49932, 99865, -199728, 399458, -798915, 1597830, -3195660, 6391321, -12782640, 25565282, -51130563, 102261126, -204522252, 409044505, -818089008, 1636178018, -3272356035, 6544712070
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OFFSET
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0,3
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COMMENTS
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Convolution of A010892(n) and (-1)^n*A001045(n+1). The positive sequence has g.f. 1/((1-x-2x^2)(1+x+x^2)). This is the convolution of A001045(n+1) and A049347(n). - Paul Barry, May 19 2004
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LINKS
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Table of n, a(n) for n=0..34.
Index to sequences with linear recurrences with constant coefficients, signature (0,2,-3,2)
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FORMULA
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G.f. : 1/((1+x-2x^2)(1-x+x^2)); a(n)=sum{k=0..n, (2*(-2)^k/3+1/3)2sin(pi*(n-k)/3+pi/3)/sqrt(3)}; a(n)=2^(n+3)cos(pi*n)/21+8sqrt(3)cos(pi*n/3+pi/6)/63+4sqrt(3)sin(pi*n/3+pi/3)/63 +2sqrt(3)sin(pi*n/3)/9+1/3; - Paul Barry, May 19 2004
a(n) = 1/3 +(-1)^n*2^(n+3)/21 - A117373(n+1)/7. - R. J. Mathar, Sep 27 2012
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CROSSREFS
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Sequence in context: A045761 A187741 A216632 * A038086 A032305 A032218
Adjacent sequences: A077900 A077901 A077902 * A077904 A077905 A077906
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane, Nov 17 2002
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STATUS
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approved
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