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A125235 Triangle with the partial column sums of the octagonal numbers.

%I A125235 #16 Jul 07 2022 20:18:33
%S A125235 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 A125235 161,63,13,1,176,364,476,406,224,76,14,1,225,540,840,882,630,300,90,
%U A125235 15,1,280,765,1380,1722,1512,930,390,105,16,1
%N A125235 Triangle with the partial column sums of the octagonal numbers.
%C A125235 "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 A125235 Row sums are 1, 9, 31, 81, 187, 405, 847 = 7*(2^n-1) - 6*n. - _R. J. Mathar_, Sep 06 2011
%D A125235 Albert H. Beiler, Recreations in the Theory of Numbers, Dover (1966), p. 189.
%F A125235 T(n,1) = A000567(n).
%F A125235 T(n,k) = T(n-1,k-1) + T(n-1,k), k>1.
%F A125235 T(n,2) = A002414(n-1).
%F A125235 T(n,3) = A002419(n-2).
%F A125235 T(n,4) = A051843(n-4).
%F A125235 T(n,5) = A027810(n-6).
%e A125235 First few rows of the triangle:
%e A125235    1;
%e A125235    8,   1;
%e A125235   21,   9,   1;
%e A125235   40,  30,  10,   1;
%e A125235   65,  70,  40,  11,   1;
%e A125235   96, 135, 110,  51,  12,   1;
%e A125235   ...
%o A125235 (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 A125235 tabl(nn) = {for (n = 1, nn, for (k = 1, n, print1(t(n, k), ", ");); print(););} \\ _Michel Marcus_, Mar 04 2014
%Y A125235 Cf. A000567, A002414, A002419, A051843, A027810, A125232 - A125234.
%K A125235 nonn,tabl,easy
%O A125235 1,2
%A A125235 _Gary W. Adamson_, Nov 24 2006
%E A125235 More terms from _Michel Marcus_, Mar 04 2014