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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 Table of n, a(n) for n=0..35. 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 Cf. A163626, A308326. Sequence in context: A098494 A008955 A182824 * A152862 A348014 A108440 Adjacent sequences: A329117 A329118 A329119 * A329121 A329122 A329123 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.)