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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. 0
 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 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 CROSSREFS Sequence in context: A065457 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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