OFFSET
0,2
COMMENTS
Riordan array (1/(1-4*x+x^2), x/(1-4*x+x^2)).
Subtriangle of the triangle given by (0, 4, -1/4, 1/4, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
For 1<=k<=n, T(n,k) equals the number of (n-1)-length words over {0,1,2,3,4} containing k-1 letters equal 4 and avoiding 01. - Milan Janjic, Dec 20 2016
LINKS
Rigoberto Flórez, Leandro Junes, José L. Ramírez, Further Results on Paths in an n-Dimensional Cubic Lattice, J. Int. Seq. 21 (2018), #18.1.2.
Milan Janjić, Words and Linear Recurrences, J. Int. Seq. 21 (2018), #18.1.4.
FORMULA
EXAMPLE
Triangle begins:
1
4, 1
15, 8, 1
56, 46, 12, 1
209, 232, 93, 16, 1
780, 1091, 592, 156, 20, 1
2911, 4912, 3366, 1200, 235, 24, 1
10864, 21468, 17784, 8010, 2120, 330, 28, 1
40545, 91824, 89238, 48624, 16255, 3416, 441, 32, 1
151316, 386373, 430992, 275724, 111524, 29589, 5152, 568, 36, 1
...
Triangle (0, 4, -1/4, 1/4, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:
1
0, 1
0, 4, 1
0, 15, 8, 1
0, 56, 46, 12, 1
0, 209, 232, 93, 16, 1
...
MATHEMATICA
With[{n = 9}, DeleteCases[#, 0] & /@ CoefficientList[Series[1/(1 - 4 x + x^2 - y x), {x, 0, n}, {y, 0, n}], {x, y}]] // Flatten (* Michael De Vlieger, Apr 25 2018 *)
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Feb 20 2012
EXTENSIONS
Offset changed to 0 by Georg Fischer, Feb 18 2020
STATUS
approved