cp's OEIS Frontend

A329120 The q-analog T(q; n,k) of the triangle A163626 for 0 <= k <= n, for q=3.

%I A329120 #9 Dec 07 2019 00:50:47
%S A329120 1,1,-1,1,-5,4,1,-21,72,-52,1,-85,1020,-3016,2080,1,-341,13600,
%T A329120 -133900,372320,-251680,1,-1365,178164,-5532800,50406720,-136662240,
%U A329120 91611520,1,-5461,2321592,-223628132,6320525120,-55844268480,149876446720,-100131391360
%N A329120 The q-analog T(q; n,k) of the triangle A163626 for 0 <= k <= n, for q=3.
%C A329120 For more information see A308326. There you'll find formulas for the general case depending on some fixed integer q.
%e A329120 The triangle T(3; n,k) starts:
%e A329120 n\ k: 0     1      2        3        4          5        6
%e A329120 ==========================================================
%e A329120    0: 1
%e A329120    1: 1    -1
%e A329120    2: 1    -5      4
%e A329120    3: 1   -21     72      -52
%e A329120    4: 1   -85   1020    -3016     2080
%e A329120    5: 1  -341  13600  -133900   372320    -251680
%e A329120    6: 1 -1365 178164 -5532800 50406720 -136662240 91611520
%e A329120 etc.
%o A329120 (PARI)  { T(n,k) = if( k<0 || k>n, 0, if( k==0, 1, (3^(k+1) - 1)/2 * T(n-1,k) - (3^k - 1)/2 * T(n-1,k-1)))};
%o A329120 for(n=0, 7, for(k=0, n, print1(T(n,k), ", ")))
%Y A329120 Cf. A163626, A308326.
%K A329120 sign,tabl
%O A329120 0,5
%A A329120 _Werner Schulte_, Nov 05 2019