OFFSET
0,6
LINKS
Lars Blomberg, Table of n, a(n) for n = 0..1680 (rows 0-40)
Johann Cigler, Some remarks and conjectures related to lattice paths in strips along the x-axis, arXiv:1501.04750 [math.CO], 2015-2016.
EXAMPLE
Triangle begins:
1,
1,1,1,
1,2,4,1,1,
1,3,9,5,7,1,1,
1,4,16,14,26,8,10,1,1,
1,5,25,30,70,34,52,11,13,1,1,
1,6,36,55,155,104,190,63,87,14,16,1,1
1,7,49,91,301,259,553,253,403,101,131,17,19,1,1
1,8,64,140,532,560,1372,806,1462,504,736,148,184,20,22,1,1
...
MATHEMATICA
T[_, 0] = 1; T[j_, k_] /; 0 <= k <= 2j := T[j, k] = Which[k<0 || k>2j, 0, k == 2j || k == 2j-1, 1, OddQ[k], T[j-1, k] + T[j-1, k-1], EvenQ[k], T[j-1, k-2] + 2 T[j-1, k-1] + T[j-1, k]];
Table[T[j, k], {j, 0, 8}, {k, 0, 2j}] // Flatten (* Jean-François Alcover, Oct 09 2018 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Sep 23 2014
EXTENSIONS
More terms from Lars Blomberg, Aug 05 2015
STATUS
approved