A256275 - OEIS

%I #24 Sep 08 2022 08:46:11

%S 0,6,238,31710,16510910,34089189246,280371153272574,

%T 9205322385119247870,1207744073945406663293950,

%U 633515663914742881158342637566,1328903397983747395279166325955489790,11149011303623843458013522930838119932485630,374121581799746201009538413109130562019709006364670

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

%H Stuart Bruff, <a href="/A256275/b256275.txt">Table of n, a(n) for n = 1..26</a>

%F a(n) = 2^(n^2) - (1 + (2^((n+1)*(n-1)) + 2^((n+1)*(n-2) + .. 1))).

%F a(n) = 2^(n^2) - (1 + A119408(n)).

%F a(n) = ((2^(n^2) - 2)*(2^n - 1))/(2*2^n - 1)

%e For n = 3, a(3) = 2^(3^2) - (1 + (2^((3+1)*(3-1)) + 2^((3+1)*(3-2)) + 2^((3+1)*(3-3)))) = 2^9  - (1 + (2^8 + 2^4 + 2^0)) = 512 - (1 + (256 + 16 + 1)) = 512 - 274 = 238.

%p seq((2^(n^2)-2)*(1-2^n)/(1-2^(n+1)),n=1..26); # _Robert Israel_, Jun 02 2015

%t Table[2^(n^2) - (1 + Sum[2^((n + 1) (n - k)), {k, n}]), {n, 12}] (* _Michael De Vlieger_, Jun 02 2015 *)

%o (Mathcad) 2^(n^2) - (1 + Summation[k=1..n (2^((n+1).(n-k)))])

%o (Magma) [(2^(n^2)-2)*(1-2^n)/(1-2^(n+1)): n in [1..15]]; // _Vincenzo Librandi_, Jun 03 2015

%Y Cf. A119408.

%K nonn

%O 1,2

%A _Stuart Bruff_, Jun 02 2015