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Triangle read by rows: A000012 * A115361 as infinite lower triangular matrices.
1

%I #13 Jul 04 2023 10:12:19

%S 1,2,1,2,1,1,3,2,1,1,3,2,1,1,1,3,2,2,1,1,1,3,2,2,1,1,1,1,4,3,2,2,1,1,

%T 1,1,4,3,2,2,1,1,1,1,1,4,3,2,2,2,1,1,1,1,1,4,3,2,2,2,1,1,1,1,1,1,4,3,

%U 3,2,2,2,1,1,1,1,1,1

%N Triangle read by rows: A000012 * A115361 as infinite lower triangular matrices.

%C Triangle read by rows, A000012 * A115361; where A000012 = an infinite lower triangular matrix with all 1's: [1; 1,1; 1,1,1; ...] and A115361 = the ruler function triangle.

%C The operation A000012 * A115361 takes partial sums of A115361 column terms starting from the top. [_Gary W. Adamson_, Nov 27 2009]

%C Eigensequence of the triangle = A089067: (1, 3, 5, 13, 23, 51, 97, 207, ...). [_Gary W. Adamson_, Nov 27 2009]

%C Row sums = A005187: (1, 3, 4, 7, 8, 10, 11, 15, ...).

%C Left column = A070939 starting (1, 2, 2, 3, 3, 3, 3, 4, 4, 4, ...).

%e First few rows of the triangle:

%e 1;

%e 2, 1;

%e 2, 1, 1;

%e 3, 2, 1, 1;

%e 3, 2, 1, 1, 1;

%e 3, 2, 2, 1, 1, 1;

%e 3, 2, 2, 1, 1, 1, 1;

%e 4, 3, 2, 2, 1, 1, 1, 1;

%e 4, 3, 2, 2, 1, 1, 1, 1, 1;

%e 4, 3, 2, 2, 2, 1, 1, 1, 1, 1;

%e 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1;

%e 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1;

%e ...

%Y Cf. A000012, A005187, A070939, A089067, A115361, A129265.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Apr 06 2007

%E Incorrect a(79) removed by _Georg Fischer_, Jul 04 2023