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

0,2

Links

Table of n, a(n) for n=0..32.

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

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

Sequence in context: A296946 A096227 A191309 * A134353 A280229 A360323

Adjacent sequences: A323348 A323349 A323350 * A323352 A323353 A323354

Keyword

nonn

Author

Gus Wiseman, Jan 15 2019

Status

approved