OFFSET
0,2
FORMULA
Recurrence: T(0,0)=1, T(0,k)=0 for k>0 and for n>=1 T(n,k) = T(n-1,k-1)+3*T(n-1,k)+3*T(n-1,k+1).
EXAMPLE
[0] [1]
[1] [3, 1]
[2] [12, 6, 1]
[3] [54, 33, 9, 1]
[4] [261, 180, 63, 12, 1]
[5] [1323, 990, 405, 102, 15, 1]
[6] [6939, 5508, 2511, 756, 150, 18, 1]
[7] [37341, 30996, 15309, 5229, 1260, 207, 21, 1]
MATHEMATICA
T[0, 0] = 1; T[n_, n_] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = T[n - 1, k - 1] + 3*T[n - 1, k] + 3*T[n - 1, k + 1]; T[_, _] = 0;
Table[T[n, k], {n, 0, 9}, {k, 0, n}] (* Jean-François Alcover, Jun 29 2019 *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 20 2012
STATUS
approved