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A007318 * a bidiagonal matrix with all 1's in the main diagonal and all 4's in the subdiagonal.
1

%I #12 Jul 26 2023 21:09:31

%S 1,5,1,9,6,1,13,15,7,1,17,28,22,8,1,21,45,50,30,9,1,25,66,95,80,39,10,

%T 1,29,91,161,175,119,49,11,1,33,120,252,336,294,168,60,12,1,37,153,

%U 372,588,630,462,228,72,13,1

%N A007318 * a bidiagonal matrix with all 1's in the main diagonal and all 4's in the subdiagonal.

%C Row sums = A048487.

%C When the first column is removed from this triangle, the result is A125233. - _Georg Fischer_, Jul 26 2023

%F Binomial transform of an infinite lower triangular matrix with all 1's in the main diagonal and all 4's in the subdiagonal (by columns, (1, 4, 0, 0, 0, ...) in every column.

%e First few rows of the triangle:

%e 1;

%e 5, 1;

%e 9, 6, 1;

%e 13, 15, 7, 1;

%e 17, 28, 22, 8, 1;

%e 21, 45, 50, 30, 9, 1;

%e 25, 66, 95, 80, 39, 10, 1;

%e ...

%Y Cf. A048487, A125233.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Dec 01 2007