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A261819
Encoded symmetrical antidiagonal square binary matrices with either 1 or 2 ones.
1
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.
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
KEYWORD
nonn
AUTHOR
Eric Werley, Sep 24 2015
STATUS
approved