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A323351
Number of ways to fill a (not necessarily square) matrix with n zeros and ones.
13
1, 2, 8, 16, 48, 64, 256, 256, 1024, 1536, 4096, 4096, 24576, 16384, 65536, 131072, 327680, 262144, 1572864, 1048576, 6291456, 8388608, 16777216, 16777216, 134217728, 100663296, 268435456, 536870912, 1610612736, 1073741824, 8589934592, 4294967296, 25769803776
OFFSET
0,2
FORMULA
a(n) = 2^n * A000005(n) for n > 0, a(0) = 1.
G.f.: 1 + Sum_{k>=1} 2^k*x^k/(1 - 2^k*x^k). - Ilya Gutkovskiy, May 23 2019
EXAMPLE
The a(3) = 16 matrices:
[000] [001] [010] [011] [100] [101] [110] [111]
.
[0] [0] [0] [0] [1] [1] [1] [1]
[0] [0] [1] [1] [0] [0] [1] [1]
[0] [1] [0] [1] [0] [1] [0] [1]
MATHEMATICA
Table[2^n*DivisorSigma[0, n], {n, 10}]
PROG
(PARI) a(n) = if (n==0, 1, 2^n*numdiv(n)); \\ Michel Marcus, Jan 15 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2019
STATUS
approved