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%I #7 Sep 08 2022 08:45:50
%S 1,1,1,1,325,1,1,178849,178849,1,1,1121470273,1106493697,1121470273,1,
%T 1,65131063096321,64859828626945,64859828626945,65131063096321,1,1,
%U 34423599076368353281,34376183545107456001,34376383642256188417,34376183545107456001,34423599076368353281,1
%N Triangle 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, read by rows.
%H G. C. Greubel, <a href="/A172198/b172198.txt">Rows n = 0..30 of the triangle, flattened</a>
%F 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 = 3.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 325, 1;
%e 1, 178849, 178849, 1;
%e 1, 1121470273, 1106493697, 1121470273, 1;
%e 1, 65131063096321, 64859828626945, 64859828626945, 65131063096321, 1;
%t T[n_, k_, q_]:= 1 + Abs[QPochhammer[q,q,n] -QPochhammer[q,q,k]]*Abs[QPochhammer[q, q, n] - QPochhammer[q,q,n-k]];
%t Table[T[n,k,3], {n,0,10}, {k,0,n}]//TableForm (* modified by _G. C. Greubel_, May 06 2021 *)
%o (Magma)
%o c:= func< n,q | n eq 0 select 1 else (&*[1-q^j: j in [1..n]]) >;
%o T:= func< n,k,q | 1 + Abs(c(n,q) - c(k,q))*Abs(c(n,q) - c(n-k,q)) >;
%o [T(n,k,3): k in [0..n], n in [0..10]]; // _G. C. Greubel_, May 06 2021
%o (Sage)
%o from sage.combinat.q_analogues import q_pochhammer
%o 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))
%o [[T(n,k,3) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, May 06 2021
%Y Cf. A172196 (q=2), this sequence (q=3).
%K nonn,tabl,less,easy
%O 0,5
%A _Roger L. Bagula_, Jan 29 2010
%E Edited by _G. C. Greubel_, May 06 2021
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