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A143037 Triangle read by rows, A000012 * A127773 * A000012. A000012 = an infinite lower triangular matrix with all 1's, A127773 = (1; 0,3; 0,0,6; 0,0,0,10;...). 3

%I

%S 1,3,4,6,9,10,10,16,19,20,15,25,31,34,35,21,36,46,52,55,56,28,49,64,

%T 74,80,83,84,36,64,85,100,110,116,119,120,45,81,109,130,145,155,161,

%U 164,165,55,100,136,164,185,200,210,216,219,220

%N Triangle read by rows, A000012 * A127773 * A000012. A000012 = an infinite lower triangular matrix with all 1's, A127773 = (1; 0,3; 0,0,6; 0,0,0,10;...).

%C Right border = tetrahedral numbers, left border = triangular numbers.

%C Alternatively this is the square array A(n,k)

%C 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,..

%C 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,..

%C 10, 19, 31, 46, 64, 85, 109, 136, 166, 199,..

%C 20, 34, 52, 74, 100, 130, 164, 202, 244, 290,..

%C 35, 55, 80, 110, 145, 185, 230, 280, 335, 395,..

%C 56, 83, 116, 155, 200, 251, 308, 371, 440, 515,..

%C read by antidiagonals where A(n,k) = n*(n^2+3*k*n+3*k^2-1)/6 is the sum of n triangular numbers starting at A000217(k). - _R. J. Mathar_, May 06 2015

%e First few rows of the triangle are:

%e 1;

%e 3, 4;

%e 6, 9, 10;

%e 10, 16, 19, 20;

%e 15, 25, 31, 34, 35;

%e 21, 36, 46, 52, 55, 56;

%e 28, 49, 64, 74, 80, 83, 84;

%e 36, 64, 85, 100, 110, 116, 119, 120;

%e ...

%Y Cf. A001296 (row sums).

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_ & _Roger L. Bagula_, Jul 18 2008

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)