OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..30 of the triangle, flattened
FORMULA
T(n, k, q) = 1 + abs(c(n,q) - c(k,q))*abs(c(n,q) - c(n-k, q)), where c(n,q) = Product_{j=1..n} (1 - q^j) and q = 2.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 17, 1;
1, 481, 481, 1;
1, 106177, 97345, 106177, 1;
1, 98421121, 95179393, 95179393, 98421121, 1;
1, 384472892161, 378269256961, 378490726657, 378269256961, 384472892161, 1;
MATHEMATICA
T[n_, k_, q_]:= 1 +Abs[QPochhammer[q, q, n] -QPochhammer[q, q, k]]*Abs[QPochhammer[q, q, n] -QPochhammer[q, q, n-k]];
Table[T[n, k, 2], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 06 2021 *)
PROG
(Magma)
c:= func< n, q | n eq 0 select 1 else (&*[1-q^j: j in [1..n]]) >;
T:= func< n, k, q | 1 + Abs(c(n, q) - c(k, q))*Abs(c(n, q) - c(n-k, q)) >;
[T(n, k, 2): k in [0..n], n in [0..10]]; // G. C. Greubel, May 06 2021
(Sage)
from sage.combinat.q_analogues import q_pochhammer
def T(n, k, q): return 1 + abs(q_pochhammer(n, q, q) -q_pochhammer(k, q, q))*abs(q_pochhammer(n, q, q) -q_pochhammer(n-k, q, q))
flatten([[T(n, k, 2) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, May 06 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Jan 29 2010
EXTENSIONS
Edited by G. C. Greubel, May 06 2021
STATUS
approved