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A247622 Triangular array:  T(n,k) = number of paths from (0,0) to (n,k), each segment given by a vector (1,1), (1,-1), or (2,0), not crossing the x-axis, and including no horizontal segment on the x-axis. 2
1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 3, 0, 5, 0, 1, 0, 11, 0, 7, 0, 1, 11, 0, 23, 0, 9, 0, 1, 0, 45, 0, 39, 0, 11, 0, 1, 45, 0, 107, 0, 59, 0, 13, 0, 1, 0, 197, 0, 205, 0, 83, 0, 15, 0, 1, 197, 0, 509, 0, 347, 0, 111, 0, 17, 0, 1, 0, 903, 0, 1061, 0, 541, 0, 143, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..1000

EXAMPLE

First 9 rows:

1

0 ... 1

1 ... 0 ... 1

0 ... 3 ... 0 ... 1

3 ... 0 ... 5 ... 0 ... 1

0 ... 11 .. 0 ... 7 ... 0 ...1

11 .. 0 ... 23 .. 0 ... 9 ... 0 ... 1

0 ... 45 .. 0 ... 39 .. 0 ... 11 .. 0 ... 1

45 .. 0 ... 107 . 0 ... 59 .. 0 ... 13 .. 0 ... 1

T(3,1) counts these 3 paths given as vector sums applied to (0,0):

(1,1) + (1,-1), (2,0), (1,-1) + (1,1).

MATHEMATICA

t[0, 0] = 1; t[1, 1] = 1; t[2, 0] = 1; t[2, 2] = 1; t[n_, k_] := t[n, k] = If[n >= 2 && k >= 1, t[n - 1, k - 1] + t[n - 1, k + 1] + t[n - 2, k], 0]; t[n_, 0] := t[n, 0] = t[n - 1, 1]; u = Table[t[n, k], {n, 0, 16}, {k, 0, n}];

v = Flatten[u] (* A247622 sequence *)

TableForm[u]   (* A247622 array *)

Map[Total, u]  (* A247623 *)

CROSSREFS

Cf. A247623, A247629, A026300, A001003 (1st column of this triangle).

Sequence in context: A035653 A126595 A286096 * A256037 A179898 A066325

Adjacent sequences:  A247619 A247620 A247621 * A247623 A247624 A247625

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Sep 21 2014

STATUS

approved

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Last modified November 16 22:10 EST 2018. Contains 317275 sequences. (Running on oeis4.)