A275779 a(n) = (2^(n^2) - 1)/(1 - 1/2^n).

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

Offset: 1

Author

Olivier Gérard, Aug 08 2016

Keywords

• nonn
• easy

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

Crossrefs

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

Cf. A096131, A057524.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

Terms a(11) and beyond from Andrew Howroyd, Apr 26 2020