A275779 - OEIS

A275779

a(n) = (2^(n^2) - 1)/(1 - 1/2^n).

2, 20, 584, 69904, 34636832, 69810262080, 567382630219904, 18519084246547628288, 2422583247133816584929792, 1268889750375080065623288448000, 2659754699919401766201267083003561984, 22306191045953951743035482794815064402563072

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OFFSET

1,1

COMMENTS

Sum of the geometric progression of ratio 2^n.

Number of all partial binary matrices with rows of length n: A partial binary matrix has 1<=k<=n rows of length n. The number of different partial matrices with k rows is 2^(k*n). a(n) is the sum for k between 1 and n.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50

FORMULA

a(n) = Sum_{k=1..n} 2^(k*n).

MATHEMATICA

Table[(2^(n^2) - 1)/(1 - 1/2^n), {n, 1, 10}]

PROG

(PARI) a(n) = {(2^(n^2) - 1)/(1 - 1/2^n)} \\ Andrew Howroyd, Apr 26 2020

CROSSREFS

Cf. A128889 (accepting the null matrix and excluding the full n*n matrices)

Cf. A096131, A057524.

Sequence in context: A157317 A350794 A009399 * A292415 A197743 A009182