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A329120 The q-analog T(q; n,k) of the triangle A163626 for 0 <= k <= n, for q=3. 0
1, 1, -1, 1, -5, 4, 1, -21, 72, -52, 1, -85, 1020, -3016, 2080, 1, -341, 13600, -133900, 372320, -251680, 1, -1365, 178164, -5532800, 50406720, -136662240, 91611520, 1, -5461, 2321592, -223628132, 6320525120, -55844268480, 149876446720, -100131391360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
For more information see A308326. There you'll find formulas for the general case depending on some fixed integer q.
LINKS
EXAMPLE
The triangle T(3; n,k) starts:
n\ k: 0 1 2 3 4 5 6
==========================================================
0: 1
1: 1 -1
2: 1 -5 4
3: 1 -21 72 -52
4: 1 -85 1020 -3016 2080
5: 1 -341 13600 -133900 372320 -251680
6: 1 -1365 178164 -5532800 50406720 -136662240 91611520
etc.
PROG
(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)))};
for(n=0, 7, for(k=0, n, print1(T(n, k), ", ")))
CROSSREFS
Sequence in context: A098494 A008955 A182824 * A152862 A348014 A108440
KEYWORD
sign,tabl
AUTHOR
Werner Schulte, Nov 05 2019
STATUS
approved

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Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)