A247645 Triangle read by rows: T(j,0)=1, T(0,j) = [j=0], T(-1,j)=T(-2,j)=0, T(j,k)=2T(j-1,k)-T(j-2,k)+T(j-1,k-2)+T(j-2,k-2).

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

Offset: 0

Author

N. J. A. Sloane, Sep 23 2014

Keywords

• nonn
• tabf

Examples

			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
...
		

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.

Crossrefs

Column 0-5 is A000012, A000027, A000290, A000330, A006325, A033455.

Programs

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 *)

Extensions

More terms from Lars Blomberg, Aug 05 2015