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

%I #9 Dec 07 2019 00:50:47

%S 1,1,-1,1,-5,4,1,-21,72,-52,1,-85,1020,-3016,2080,1,-341,13600,

%T -133900,372320,-251680,1,-1365,178164,-5532800,50406720,-136662240,

%U 91611520,1,-5461,2321592,-223628132,6320525120,-55844268480,149876446720,-100131391360

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

%C For more information see A308326. There you'll find formulas for the general case depending on some fixed integer q.

%e The triangle T(3; n,k) starts:

%e n\ k: 0 1 2 3 4 5 6

%e ==========================================================

%e 0: 1

%e 1: 1 -1

%e 2: 1 -5 4

%e 3: 1 -21 72 -52

%e 4: 1 -85 1020 -3016 2080

%e 5: 1 -341 13600 -133900 372320 -251680

%e 6: 1 -1365 178164 -5532800 50406720 -136662240 91611520

%e etc.

%o (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 for(n=0, 7, for(k=0, n, print1(T(n,k), ", ")))

%Y Cf. A163626, A308326.

%K sign,tabl

%O 0,5

%A _Werner Schulte_, Nov 05 2019

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Last modified April 24 03:08 EDT 2024. Contains 371918 sequences. (Running on oeis4.)