OFFSET
0,2
COMMENTS
A triangular sequence formed from the omega2 Jacobian Elliptic Modular function.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5150
Eric Weisstein's World of Mathematics, Modular Equation
FORMULA
T(n, k) = k^2*(1+n)^2 - 4*n.
Sum_{k=0..n} T(n, k) = (n*(n+1)/6)*( 2*n^3 + 5*n^2 + 4*n - 23 ). (n+1)^2 * A000330(n) - 8 * A000217(n). - G. C. Greubel, Feb 19 2021
EXAMPLE
Triangle begins:
0;
-4, 0;
-8, 1, 28;
-12, 4, 52, 132;
-16, 9, 84, 209, 384;
-20, 16, 124, 304, 556, 880;
-24, 25, 172, 417, 760, 1201, 1740;
-28, 36, 228, 548, 996, 1572, 2276, 3108;
-32, 49, 292, 697, 1264, 1993, 2884, 3937, 5152;
-36, 64, 364, 864, 1564, 2464, 3564, 4864, 6364, 8064;
-40, 81, 444, 1049, 1896, 2985, 4316, 5889, 7704, 9761, 12060;
MATHEMATICA
T[n_, k_]:= k^2*(1+n)^2 - 4*n;
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Sage) flatten([[k^2*(n+1)^2 - 4*n for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 19 2021
(Magma) [k^2*(n+1)^2 - 4*n: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 19 2021
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Oct 28 2006
EXTENSIONS
Edited by G. C. Greubel, Feb 19 2021
STATUS
approved