OFFSET
0,5
LINKS
T. D. Noe, Rows n = 0..100 of triangle, flattened
Eric Weisstein's World of Mathematics, Polygonal Number
FORMULA
Array of coefficients of x in the expansions of T(k, x) = (1 + k*x -(k-2)*x^2)/(1-x)^4, k > -4.
T(n, k) = k*((n-2)*k -(n-4))/2 (see MathWorld link). - Michel Marcus, Jun 22 2015
EXAMPLE
The array starts
1 1 3 10 ...
1 2 6 16 ...
1 3 9 22 ...
1 4 12 28 ...
The triangle starts
1;
1, 1;
1, 2, 3;
1, 3, 6, 10;
1, 4, 9, 16, 25;
...
MATHEMATICA
Table[PolygonalNumber[n, i], {n, 0, 10}, {i, n+1}]//Flatten (* Requires Mathematica version 10.4 or later *) (* Harvey P. Dale, Aug 27 2016 *)
PROG
(PARI) tabl(nn) = {for (n=0, nn, for (k=1, n+1, print1(k*((n-2)*k-(n-4))/2, ", "); ); print(); ); } \\ Michel Marcus, Jun 22 2015
(Magma) [[k*((n-2)*k-(n-4))/2: k in [1..n+1]]: n in [0..10]]; // G. C. Greubel, Oct 13 2018
(Sage) [[k*((n-2)*k -(n-4))/2 for k in (1..n+1)] for n in (0..10)] # G. C. Greubel, Aug 14 2019
(GAP) Flat(List([0..10], n-> List([1..n+1], k-> k*((n-2)*k-(n-4))/2 ))); # G. C. Greubel, Aug 14 2019
CROSSREFS
AUTHOR
Paul Barry, Mar 21 2003
STATUS
approved