A174377 - OEIS

%I #8 Nov 29 2021 01:05:24

%S 1,1,1,1,6,1,1,9,9,1,1,12,108,12,1,1,15,180,180,15,1,1,18,270,3240,

%T 270,18,1,1,21,378,5670,5670,378,21,1,1,24,504,9072,136080,9072,504,

%U 24,1,1,27,648,13608,244944,244944,13608,648,27,1,1,30,810,19440,408240,7348320,408240,19440,810,30,1

%N Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 3, read by rows.

%C Row sums are: {1, 2, 8, 20, 134, 392, 3818, 12140, 155282, 518456, 8205362, ...}.

%H G. C. Greubel, <a href="/A174377/b174377.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 3.

%F T(n, n-k) = T(n, k).

%F T(2*n, n) = A221954(n+1). - _G. C. Greubel_, Nov 28 2021

%e Triangle begins as:

%e   1;

%e   1,  1;

%e   1,  6,   1;

%e   1,  9,   9,     1;

%e   1, 12, 108,    12,      1;

%e   1, 15, 180,   180,     15,       1;

%e   1, 18, 270,  3240,    270,      18,      1;

%e   1, 21, 378,  5670,   5670,     378,     21,     1;

%e   1, 24, 504,  9072, 136080,    9072,    504,    24,   1;

%e   1, 27, 648, 13608, 244944,  244944,  13608,   648,  27,  1;

%e   1, 30, 810, 19440, 408240, 7348320, 408240, 19440, 810, 30,  1;

%t T[n_, k_, q_]:= If[Floor[n/2]>=k, n!*q^k/(n-k)!, n!*q^(n-k)/k!];

%t Table[T[n, k, 3], {n,0,12}, {k,0,n}]//Flatten

%o (Sage)

%o f=factorial

%o def T(n,k,q): return f(n)*q^k/f(n-k) if ((n//2)>k-1) else f(n)*q^(n-k)/f(k)

%o flatten([[T(n,k,3) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Nov 28 2021

%Y Cf. A159623 (q=1), A174376 (q=2), this sequence (q=3), A174378 (q=4).

%Y Cf. A221954.

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Mar 17 2010

%E Edited by _G. C. Greubel_, Nov 28 2021