OFFSET
1,2
COMMENTS
"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.
Row sums are 1, 9, 31, 81, 187, 405, 847 = 7*(2^n-1) - 6*n. - R. J. Mathar, Sep 06 2011
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover (1966), p. 189.
FORMULA
EXAMPLE
First few rows of the triangle:
1;
8, 1;
21, 9, 1;
40, 30, 10, 1;
65, 70, 40, 11, 1;
96, 135, 110, 51, 12, 1;
...
PROG
(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))));
tabl(nn) = {for (n = 1, nn, for (k = 1, n, print1(t(n, k), ", "); ); print(); ); } \\ Michel Marcus, Mar 04 2014
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Nov 24 2006
EXTENSIONS
More terms from Michel Marcus, Mar 04 2014
STATUS
approved