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%I #13 Feb 07 2022 02:42:34
%S 1,5,3,12,9,5,22,18,13,7,35,30,24,17,9,51,45,38,30,21,11,70,63,55,46,
%T 36,25,13,92,84,75,65,54,42,29,15,117,108,98,87,75,62,48,33,17,145,
%U 135,124,112,99,85,70,54,37,19,176,165,153,140,126,111,95,78,60,41,21
%N Triangle read by rows, given by the matrix product A * B where A (A094727) = [1; 2, 3; 3, 4, 5; 4, 5, 6, 7; ...] and B = [1; 1, 1; 1, 1, 1; ...] (both are infinite lower triangular matrices with the other terms zero).
%C Left column of the triangle = pentagonal numbers, A000326 (starting with 1).
%C Row sums = heptagonal pyramidal numbers, A002413.
%e Triangle begins:
%e 1;
%e 5, 3;
%e 12, 9, 5;
%e 22, 18, 13, 7;
%e 35, 30, 24, 17, 9;
%e 51, 45, 38, 30, 21, 11;
%e 70, 63, 55, 46, 36, 25, 13;
%e 92, 84, 75, 65, 54, 42, 29, 15;
%e ...
%o (PARI) tabl(nn) = {ma = matrix(nn, nn, n, k, (n+k-1)*(k<=n)); mb = matrix(nn, nn, n, k, (k<=n)); mt = ma*mb; for (i=1, nn, for (j=1, i, print1(ma[i,j], ", ");); print(););} \\ _Michel Marcus_, Mar 03 2014
%Y Cf. A000326, A094727, A002413.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Mar 17 2005
%E More terms from _Michel Marcus_, Mar 03 2014
%E Edited by _Michel Marcus_ and _N. J. A. Sloane_, Mar 03 2014
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