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A102437 Let pi be an unrestricted partition of n with the summands written in binary notation. a(n) is the number of such partitions whose binary representation has an odd number of binary ones. 3
0, 1, 1, 1, 3, 3, 5, 9, 10, 14, 22, 28, 37, 53, 66, 85, 120, 147, 188, 252, 308, 394, 509, 621, 783, 990, 1210, 1500, 1872, 2272, 2793, 3447, 4152, 5064, 6184, 7414, 8984, 10856, 12964, 15592, 18711, 22250, 26576, 31690, 37520, 44565, 52856, 62292 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

EXAMPLE

a(5) = 3 because there are 3 partitions of 5 with an odd number of binary ones in their binary representation, namely: 11+10, 10+10+1 and 1+1+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 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]]], OddQ[Count[#, 1]]&]], {n, 0, 40}] (* Geoffrey Critzer, Sep 28 2013 *)

PROG

(PARI) seq(n)={apply(t->polcoeff(lift(t), 1), 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, A102425, A316996.

Sequence in context: A136791 A213933 A091916 * A319794 A072706 A117433

Adjacent sequences:  A102434 A102435 A102436 * A102438 A102439 A102440

KEYWORD

nonn

AUTHOR

David S. Newman, Feb 23 2005

EXTENSIONS

More terms from Vladeta Jovovic, Feb 23 2005

STATUS

approved

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Last modified December 12 18:24 EST 2018. Contains 318081 sequences. (Running on oeis4.)