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A072100
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Column 2 of the array m(i,1)=m(1,j)=1 m(i,j)=m(i-1,j-1)+m(i-1,j+1) (a(n)=m(n,2)).
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4
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1, 2, 3, 5, 8, 14, 24, 44, 79, 149, 275, 527, 989, 1913, 3629, 7061, 13496, 26366, 50676, 99296, 191674, 376430, 729146, 1434578, 2786656, 5490812, 10691112, 21091712, 41150012, 81266612, 158825372, 313942892, 614483087, 1215563477
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OFFSET
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1,2
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COMMENTS
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Partial sums of A001405, to which an additional leading 1 is added. - Paul Barry, Oct 12 2004
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LINKS
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FORMULA
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G.f.: 1/2*x*(((1+2*x)/(1-2*x))^(1/2)-1)/(1-x)-1. - Vladeta Jovovic, Jan 15 2004
G.f. : (sqrt(1+2x)+1/sqrt(1-2x))/((1-x)(sqrt(1+2x)+sqrt(1-2x))); a(n)=1+sum{k=0..n, binomial(n-1, floor((n-1)/2)}. - Paul Barry, Oct 12 2004
Conjecture: (-n+1)*a(n) +(n+1)*a(n-1) +2*(2*n-7)*a(n-2) +4*(-n+3)*a(n-3)=0. - R. J. Mathar, Nov 26 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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