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A102425 Let pi be an unrestricted partition of n with the summands written as binary numbers; a(n) is the number of such partitions with an even number of binary ones. 2
1, 0, 1, 2, 2, 4, 6, 6, 12, 16, 20, 28, 40, 48, 69, 91, 111, 150, 197, 238, 319, 398, 493, 634, 792, 968, 1226, 1510, 1846, 2293, 2811, 3395, 4197, 5079, 6126, 7469, 8993, 10781, 13051, 15593, 18627, 22333, 26598, 31571, 37655, 44569, 52702, 62462 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(5) = 4 because there are 4 partitions of 5 whose binary representations have an even number of binary ones, namely 101, 100+1, 11+1+1, 10+1+1+1.

MAPLE

p:= proc(n) option remember; local c, m;

      c:= 0; m:= n;

      while m>0 do c:= c +irem(m, 2, 'm') od;

      c

    end:

b:= proc(n, i, t) option remember;

      if n<0 then 0

    elif n=0 then 1-t

    elif i=0 then 0

    else b(n, i-1, t) +b(n-i, i, irem(p(i)+t, 2))

      fi

    end:

a:= n-> b(n, n, 0):

seq(a(n), n=0..60);  # Alois P. Heinz, Feb 21 2011

MATHEMATICA

Table[Length[Select[Map[Apply[Join, #]&, Map[IntegerDigits[#, 2]&, Partitions[n]]], EvenQ[Count[#, 1]]&]], {n, 0, 40}] (* Geoffrey Critzer, Sep 28 2013 *)

PROG

(PARI) seq(n)={apply(t->polcoeff(lift(t), 0), Vec(prod(i=1, n, 1/(1 - x^i*Mod( y^hammingweight(i), y^2-1 )) + O(x*x^n))))} \\ Andrew Howroyd, Jul 20 2018

CROSSREFS

Cf. A000041, A000120, A102437.

Sequence in context: A280366 A000784 A092991 * A162608 A143216 A086536

Adjacent sequences:  A102422 A102423 A102424 * A102426 A102427 A102428

KEYWORD

nonn

AUTHOR

David S. Newman, Feb 23 2005

STATUS

approved

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)