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A111414
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f(f(n+1))-f(f(n)), where f(m) = binary partition(m) = A000123(m).
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1
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2, 6, 10, 40, 80, 250, 510, 1890, 4270, 13738, 30630, 101960, 234864, 705046, 1580578, 5136840, 11991928, 36095322, 82990606, 255579576, 595920680, 1719038038, 3926998938, 11665004238, 26978093154, 75938910058, 172678519950, 489262646480, 1114189211016
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OFFSET
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0,1
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LINKS
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MAPLE
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b:= proc(n, j) option remember; local nn, r; if n<0 then 0 elif j=0 then 1 elif j=1 then n+1 elif n<j then b(n-1, j) +b(2*n, j-1) else nn:= 1 +floor(n); r:= n-nn; (nn-j) *binomial(nn, j) *add (binomial(j, h) /(nn-j+h) *b(j-h+r, j) *(-1)^h, h=0..j-1) fi end: f:= proc(n) local t; t:= ilog2(2*n+1); b(n /2^(t-1), t) end: a:= n-> f(f(n+1)) -f(f(n)): seq (a(n), n=0..50); # Alois P. Heinz, Sep 28 2011
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MATHEMATICA
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b[n_, j_] := b[n, j] = Module[{nn, r}, Which[n<0, 0, j == 0, 1, j == 1, n+1, n<j, b[n-1, j]+b[2*n, j-1], True, nn = 1+Floor[n]; r = n-nn; (nn-j)*Binomial[nn, j]*Sum[Binomial[j, h]/(nn-j+h)*b[j-h+r, j]*(-1)^h, {h, 0, j-1}]]];
f[n_] := Module[{t}, t = Length[IntegerDigits[2n+1, 2]]-1; b[n/2^(t-1), t]];
a[n_] := f[f[n+1]] - f[f[n]];
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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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