A119408 Decimal equivalent of the binary string generated by the n X n identity matrix.

1, 9, 273, 33825, 17043521, 34630287489, 282578800148737, 9241421688590303745, 1210107565283851686118401, 634134936313486520338360567809, 1329552593586084350528447794605199361, 11151733894906779683522195341810241573494785

Offset

1,2

Comments

a(n) is divisible by 2^n - 1. a(n) == n mod 2^(n+1) - 1. - Robert Israel, Jun 09 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 1..57

Formula

a(n) = 2^((n+1)(n-1)) + 2^((n+1)(n-2)) + ... + 1 where n=2,3,...

a(n) = (2^n*2^(n^2)-1)/(2*2^n-1). - Stuart Bruff, Jun 08 2015

Example

n=2: [1 0; 0 1] == 1001_2 = 9;
n=3: [1 0 0; 0 1 0; 0 0 1] == 100010001_2 = 273;
n=4: [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1] == 1000010000100001_2 = 33825.

Mathematica

For[n=2, n<=10, Print[n, " ", Sum[2^((n+1)(k-1)), {k, 1, n}]]; n++ ]
Table[FromDigits[Flatten[IdentityMatrix[n]], 2], {n, 15}] (* Harvey P. Dale, Dec 31 2021 *)

Prog

(MATLAB) for n = 1:10 bi2de((reshape(eye(n), length(eye(n))^2, 1))') end
% Kyle Stern, Dec 14 2011
(PARI) a(n)=(2^n*2^(n^2)-1)/(2*2^n-1) \\ Charles R Greathouse IV, Jun 09 2015

Crossrefs

Cf. A128889.

Sequence in context: A197981 A188812 A197768 * A295898 A330604 A336259

Adjacent sequences: A119405 A119406 A119407 * A119409 A119410 A119411

Keyword

nonn,base

Author

Lynn R. Purser, Jul 25 2006

Status

approved