|
| |
|
|
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.
|
|
0
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
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
|
|
|
CROSSREFS
| Sequence in context: A179437 A136791 A091916 * A072706 A117433 A159284
Adjacent sequences: A102434 A102435 A102436 * A102438 A102439 A102440
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David Newman (DavidSNewman(AT)hotmail.com), Feb 23 2005
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 23 2005
|
| |
|
|
