A261819 - OEIS

%I #24 Nov 30 2016 22:10:02

%S 1,6,16,40,384,576,4096,10240,17408,393216,589824,1081344,16777216,

%T 41943040,71303168,136314880,6442450944,9663676416,17716740096,

%U 34628173824,1099511627776

%N Encoded symmetrical antidiagonal square binary matrices with either 1 or 2 ones.

%C We encode square matrices that have zeros everywhere except the antidiagonal where the antidiagonal is symmetric with either 1 or 2 ones in it. We do this by reading off digits antidiagonally to get a binary number and then convert the number to a base 10 number.

%F a(n) = A261195(2^n).

%F a(n) = 2^(A000217(floor(sqrt(4*n + 1)) - 1)) * (((A262769(floor(n/2)) * 2^((floor(sqrt(4*n + 1)) - 2*A002260(+1))/2)) * (1+(-1)^(floor(sqrt(4*n + 1))))/2) + ((A262777(floor(n/2)) * 2^((floor(sqrt(4*n + 1)) - A158405(+1))/2)) * (1-(-1)^(floor(sqrt(4*n + 1))))/2)).

%e The 3 X 3 matrix

%e 0 0 0

%e 0 1 0

%e 0 0 0

%e gives 000010000. Writing this as a base 10 number gives a(2)=16.

%e The 4 X 4 matrix

%e 0 0 0 0

%e 0 0 1 0

%e 0 1 0 0

%e 0 0 0 0

%e gives 0000000110000000. Writing this as a base 10 number gives a(4)=384.

%e The 5 X 5 matrix

%e 0 0 0 0 0

%e 0 0 0 1 0

%e 0 0 0 0 0

%e 0 1 0 0 0

%e 0 0 0 0 0

%e gives 0000000000010100000000000. Writing this as a base 10 number gives a(7)=10240.

%K nonn

%O 0,2

%A _Eric Werley_, Sep 24 2015