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A077995
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Expansion of (1-x)/(1-2*x-2*x^2-x^3).
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5
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1, 1, 4, 11, 31, 88, 249, 705, 1996, 5651, 15999, 45296, 128241, 363073, 1027924, 2910235, 8239391, 23327176, 66043369, 186980481, 529374876, 1498754083, 4243238399, 12013359840, 34011950561, 96293859201, 272624979364, 771849627691, 2185243073311, 6186810381368
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OFFSET
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0,3
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COMMENTS
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Equals INVERT transform of (1, 3, 4, 4, 4,...). - Gary W. Adamson, Jan 03 2009
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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a(n) = sum(m=1..n, sum(i=0..n-m, C(m+i-1,m-1)*sum(j=0..m, C(j,n-3*m+2*j-i) *C(m,j)*2^(n-3*m+2*j-i)))), n>0, a(0)=1. - Vladimir Kruchinin, May 12 2011
G.f.: 1 + x/(G(0)-x) where G(k)= 1 - x*(2*k+2)/(1 - 1/(1 + (2*k+2)/G(k+1)));(continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 17 2012
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PROG
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(Maxima) a(n):=sum(sum(binomial(m+i-1, m-1)*sum(binomial(j, n-3*m+2*j-i) *binomial(m, j) *2^(n-3*m+2*j-i), j, 0, m) , i, 0, n-m) , m, 1, n); - Vladimir Kruchinin, May 12 2011
(PARI) Vec((1-x)/(1-2*x-2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
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CROSSREFS
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Sequence in context: A192312 A004080 A027115 * A176573 A076730 A084757
Adjacent sequences: A077992 A077993 A077994 * A077996 A077997 A077998
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KEYWORD
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nonn,easy
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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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