A247642 Triangle read by rows: T(n,2k+1) = T(n-1,2k-1)+T(n-1,2k), T(n,2k) = T(n-1,2k-2)+2T(n-1,2k-1)+T(n-1,2k).

1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 7, 5, 9, 3, 1, 1, 1, 10, 8, 26, 14, 16, 4, 1, 1, 1, 13, 11, 52, 34, 70, 30, 25, 5, 1, 1, 1, 16, 14, 87, 63, 190, 104, 155, 55, 36, 6, 1, 1, 1, 19, 17, 131, 101, 403, 253, 553, 259, 301, 91, 49, 7, 1, 1, 1, 22, 20, 184

Offset

0,7

Links

Table of n, a(n) for n=0..68.

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 1 4 2 1
1 1 7 5 9 3 1
1 1 10 8 26 14 16 4 1
1 1 13 11 52 34 70 30 25 5 1
...

Maple

A247642 := proc(n, k)
    option remember;
    if k < 0 or k > 2*n then
        return 0;
    elif k = 0 then
        return 1 ;
    end if;
    if type(k, 'odd') then
        procname(n-1, k-2)+procname(n-1, k-1) ;
    else
        procname(n-1, k-2)+2*procname(n-1, k-1)+procname(n-1, k) ;
    end if;
end proc: # R. J. Mathar, Oct 25 2014

Mathematica

T[_, 0] = 1; T[n_, k_] /; 0 <= k <= 2n := T[n, k] = If[OddQ[k], T[n-1, k-2] + T[n-1, k-1], T[n-1, k-2] + 2*T[n-1, k-1] + T[n-1, k]]; T[_, _] = 0;
Table[T[n, k], {n, 0, 8}, {k, 0, 2n}] // Flatten (* Jean-François Alcover, Dec 03 2017 *)

Crossrefs

Cf. A000244 (row sums).

Sequence in context: A303599 A068930 A204815 * A144260 A097526 A051149

Adjacent sequences: A247639 A247640 A247641 * A247643 A247644 A247645

Keyword

nonn,tabf

Author

N. J. A. Sloane, Sep 23 2014

Status

approved