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A186537
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G.f.: Sum( x^k/(1-2*x+x^k), k=1..oo).
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5
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0, 1, 2, 4, 7, 12, 20, 34, 58, 101, 178, 318, 574, 1046, 1920, 3548, 6593, 12312, 23092, 43480, 82154, 155716, 295984, 564050, 1077400, 2062311, 3955186, 7598756, 14622318, 28179338, 54379520, 105071498, 203254164, 393607534, 763001000, 1480458656, 2875091021, 5588152920, 10869906136
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OFFSET
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0,3
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COMMENTS
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This arose while studying the properties of A079500.
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LINKS
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FORMULA
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G.f.: -(1+x^2+ 1/(x-1) )/(1-x)*( 1 + x*(x-1)^3*(1-x+x^3)/( Q(0)- x*(x-1)^3*(1-x+x^3)) ), where Q(k) = (x+1)*(2*x-1)*(1-x)^2 + x^(k+2)*(x+x^2+x^3-2*x^4-1 - x^(k+3) + x^(k+5)) - x*(-1+2*x-x^(k+3))*(1-2*x+x^2+x^(k+4)-x^(k+5))*(-1+4*x-5*x^2+2*x^3 - x^(k+2)- x^(k+5) + 2*x^(k+3) - x^(2*k+5) + x^(2*k+6))/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 14 2013
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MAPLE
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add( x^k/(1-2*x+x^k), k=1..61); series(%, x, 60); seriestolist(%);
# second Maple program:
b:= proc(n, m) option remember; `if`(n=0, 1,
`if`(m=0, add(b(n-j, j), j=1..n),
add(b(n-j, min(n-j, m)), j=1..min(n, m))))
end:
a:= proc(n) a(n):= `if`(n=0, 0, b(n-1, 0)+a(n-1)) end:
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MATHEMATICA
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b[n_, m_] := b[n, m] = If[n == 0, 1, If[m == 0, Sum[b[n-j, j], {j, 1, n}], Sum[b[n-j, Min[n-j, m]], {j, 1, Min[n, m]}]]]; a[n_] := If[n == 0, 0, b[n-1, 0] + a[n-1]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 05 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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