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A111414 f(f(n+1))-f(f(n)), where f(m) = binary partition(m) = A000123(m). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2500

MAPLE

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

MATHEMATICA

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]];

Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A000123.

Sequence in context: A260559 A258079 A027165 * A308486 A202533 A275700

Adjacent sequences:  A111411 A111412 A111413 * A111415 A111416 A111417

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 12 2005

STATUS

approved

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Last modified December 4 05:56 EST 2021. Contains 349470 sequences. (Running on oeis4.)