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Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.
1

%I #6 Feb 09 2022 08:34:05

%S 1,1,1,2,1,2,3,2,2,5,4,3,4,5,12,5,4,6,10,12,28,6,5,8,15,24,28,65,7,6,

%T 10,20,36,56,65,151,8,7,12,25,48,84,130,151,351,9,8,14,30,60,112,195,

%U 302,351,816,10,9,16,35,72,140,260,453,702,816,1897

%N Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

%C Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...).

%C As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

%C A034943 starting (1, 2, 5, 12, 28, ...) = the INVERT transform of (1, 1, 2, 3, 4, 5, ...).

%F Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 2, 1, 2;

%e 3, 2, 2, 5;

%e 4, 3, 4, 5, 12;

%e 5, 4, 6, 10, 12, 28;

%e 6, 5, 8, 15, 24, 28, 65;

%e 7, 6, 10, 20, 36, 56, 65, 151;

%e 8, 7, 12, 25, 48, 84, 130, 151, 351;

%e 9, 8, 14, 30, 60, 112, 195, 302, 351, 816;

%e 10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897;

%e ...

%e Example: row 6 = (4, 3, 4, 5, 12) = termwise products of (1, 1, 2, 5, 12) and (4, 3, 2, 1, 1).

%Y Cf. A034943.

%K nonn,tabl

%O 2,4

%A _Gary W. Adamson_, Apr 28 2009