A323351 Number of ways to fill a (not necessarily square) matrix with n zeros and ones.

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

Author

Gus Wiseman, Jan 15 2019

Keywords

• nonn

Examples

			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]
		

Crossrefs

Cf. A000005, A049311, A120733, A323295, A323300.

Programs

Mathematica

Table[2^n*DivisorSigma[0,n],{n,10}]

PARI

a(n) = if (n==0, 1, 2^n*numdiv(n)); \\ Michel Marcus, Jan 15 2019

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