A119408 - OEIS

%I #26 Dec 31 2021 17:55:48

%S 1,9,273,33825,17043521,34630287489,282578800148737,

%T 9241421688590303745,1210107565283851686118401,

%U 634134936313486520338360567809,1329552593586084350528447794605199361,11151733894906779683522195341810241573494785

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

%C a(n) is divisible by 2^n - 1.  a(n) == n mod 2^(n+1) - 1. - _Robert Israel_, Jun 09 2015

%H Harvey P. Dale, <a href="/A119408/b119408.txt">Table of n, a(n) for n = 1..57</a>

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

%F a(n) = (2^n*2^(n^2)-1)/(2*2^n-1). - _Stuart Bruff_, Jun 08 2015

%e n=2: [1 0; 0 1] == 1001_2 = 9;

%e n=3: [1 0 0; 0 1 0; 0 0 1] == 100010001_2 = 273;

%e n=4: [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1] == 1000010000100001_2 = 33825.

%t For[n=2,n<=10,Print[n," ",Sum[2^((n+1)(k-1)), {k,1,n}]];n++ ]

%t Table[FromDigits[Flatten[IdentityMatrix[n]],2],{n,15}] (* _Harvey P. Dale_, Dec 31 2021 *)

%o (MATLAB) for n = 1:10 bi2de((reshape(eye(n),length(eye(n))^2,1))') end

%o % _Kyle Stern_, Dec 14 2011

%o (PARI) a(n)=(2^n*2^(n^2)-1)/(2*2^n-1) \\ _Charles R Greathouse IV_, Jun 09 2015

%Y Cf. A128889.

%K nonn,base

%O 1,2

%A _Lynn R. Purser_, Jul 25 2006