OFFSET
1,3
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = y^2*x*(x*y-4*y+x+2)/((1-y)^3*(1-x)^2). - R. J. Mathar, Nov 27 2015. x and y swapped to align with standard, 19 Feb 2020
Sum_{k=1..n} T(n, k) = (n-1)*n*(7*n+1)/6 = A245301(n-1). - G. C. Greubel, Mar 31 2021
EXAMPLE
Triangle begins as:
0;
0, 5;
0, 8, 14;
0, 11, 20, 27;
0, 14, 26, 36, 44;
0, 17, 32, 45, 56, 65;
0, 20, 38, 54, 68, 80, 90;
0, 23, 44, 63, 80, 95, 108, 119;
0, 26, 50, 72, 92, 110, 126, 140, 152;
0, 29, 56, 81, 104, 125, 144, 161, 176, 189;
MAPLE
A141431 := proc(n, k)
(k-1)*(3*n-k+1) ;
end proc:
seq(seq(A141431(n, k), k=1..n), n=1..14) ; # R. J. Mathar, Nov 10 2011
MATHEMATICA
Table[(k-1)*(3*n-k+1), {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Mar 31 2021 *)
PROG
(Magma) [(k-1)*(3*n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 31 2021
(Sage) flatten([[(k-1)*(3*n-k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 31 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula and Gary W. Adamson, Aug 06 2008
EXTENSIONS
More terms added by G. C. Greubel, Mar 31 2021
STATUS
approved