A261819 Encoded symmetrical antidiagonal square binary matrices with either 1 or 2 ones.

1, 6, 16, 40, 384, 576, 4096, 10240, 17408, 393216, 589824, 1081344, 16777216, 41943040, 71303168, 136314880, 6442450944, 9663676416, 17716740096, 34628173824, 1099511627776

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..20.

Formula

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

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)).

Example

The 3 X 3 matrix
0 0 0
0 1 0
0 0 0
gives 000010000. Writing this as a base 10 number gives a(2)=16.
The 4 X 4 matrix
0 0 0 0
0 0 1 0
0 1 0 0
0 0 0 0
gives 0000000110000000. Writing this as a base 10 number gives a(4)=384.
The 5 X 5 matrix
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
gives 0000000000010100000000000. Writing this as a base 10 number gives a(7)=10240.

Crossrefs

Sequence in context: A213667 A123205 A123607 * A347642 A073570 A283960

Adjacent sequences: A261816 A261817 A261818 * A261820 A261821 A261822

Keyword

nonn

Author

Eric Werley, Sep 24 2015

Status

approved