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Search: id:A122909
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| A122909 |
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F(n+1)F(2n+2)+F(n)F(2n). |
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+0
1
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| 1, 4, 19, 79, 338, 1427, 6053, 25628, 108583, 459931, 1948354, 8253271, 34961561, 148099316, 627359147, 2657535383, 11257501522, 47687540107, 202007664157, 855718193164, 3624880442591, 15355239954179, 65045840274434
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OFFSET
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0,2
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COMMENT
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Let M be the matrix M(n,k)=F(k+1)*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}. a(n) gives the row sums of M^3.
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FORMULA
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G.f.: (1+x+x^2+x^3)/(1-3x-6x^2+3x^3+x^4); a(n)=(sqrt(5)+2)^n(sqrt(5)/5+3/5)-2^(-n-1)(sqrt(5)-1)^n(sqrt(5)/5+1/5)+ 2^(-n-1)(sqrt(5)+1)^n(sqrt(5)/5-1/5)(-1)^n+(sqrt(5)-2)^n(3/5-sqrt(5)/5)(-1)^n;
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CROSSREFS
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Cf. A000045, A037451.
Adjacent sequences: A122906 A122907 A122908 this_sequence A122910 A122911 A122912
Sequence in context: A130132 A037590 A037681 this_sequence A027240 A050914 A017961
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 18 2006
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