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%I #16 Jul 07 2022 20:18:33
%S 1,8,1,21,9,1,40,30,10,1,65,70,40,11,1,96,135,110,51,12,1,133,231,245,
%T 161,63,13,1,176,364,476,406,224,76,14,1,225,540,840,882,630,300,90,
%U 15,1,280,765,1380,1722,1512,930,390,105,16,1
%N Triangle with the partial column sums of the octagonal numbers.
%C "Partial column sums" means the octagonal numbers are the 1st column, the 2nd column are the partial sums of the 1st column, the 3rd column are the partial sums of the 2nd, etc.
%C Row sums are 1, 9, 31, 81, 187, 405, 847 = 7*(2^n-1) - 6*n. - _R. J. Mathar_, Sep 06 2011
%D Albert H. Beiler, Recreations in the Theory of Numbers, Dover (1966), p. 189.
%F T(n,1) = A000567(n).
%F T(n,k) = T(n-1,k-1) + T(n-1,k), k>1.
%F T(n,2) = A002414(n-1).
%F T(n,3) = A002419(n-2).
%F T(n,4) = A051843(n-4).
%F T(n,5) = A027810(n-6).
%e First few rows of the triangle:
%e 1;
%e 8, 1;
%e 21, 9, 1;
%e 40, 30, 10, 1;
%e 65, 70, 40, 11, 1;
%e 96, 135, 110, 51, 12, 1;
%e ...
%o (PARI) t(n, k) = if (n <0, 0, if (k==1, n*(3*n-2), if (k > 1, t(n-1,k-1) + t(n-1,k))));
%o tabl(nn) = {for (n = 1, nn, for (k = 1, n, print1(t(n, k), ", ");); print(););} \\ _Michel Marcus_, Mar 04 2014
%Y Cf. A000567, A002414, A002419, A051843, A027810, A125232 - A125234.
%K nonn,tabl,easy
%O 1,2
%A _Gary W. Adamson_, Nov 24 2006
%E More terms from _Michel Marcus_, Mar 04 2014
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