A217315 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 8, T(0,k)= 1 if 0<=k<=7, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 4, 5, 0, 0, 0, 1, 5, 9, 5, 0, 0, 0, 1, 6, 14, 14, 0, 0, 0, 0, 0, 7, 20, 28, 14, 0, 0, 0, 0, 0, 7, 27, 48, 42, 0, 0, 0, 0, 0, 0, 0, 34, 75, 90, 42, 0, 0, 0, 0, 0, 0, 0, 34, 109, 165, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 143, 274, 297, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 143, 417, 571, 429, 0, 0, 0, 0, 0, 0, 0

Offset

0,8

Comments

A hexagon arithmetic of E. Lucas.

Links

Table of n, a(n) for n=0..104.

Formula

T(n,n) = A080938(n).

T(n,n+1) = A080938(n+1).

T(n,n+2) = A094826(n+1).

T(n,n+3) = A094827(n+1).

T(n,n+4) = A094828(n+2).

T(n,n+5) = A094829(n+2).

T(n,n+6) = T(n,n+7) = A094256(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = A061551(n).

Example

Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ... row n=0
0, 1, 2, 3, 4, 5, 6, 7, 7, 0, 0, 0, 0, 0, 0, ... row n=1
0, 0, 2, 5, 9, 14, 20, 27, 34, 34, 0, 0, 0, ... row n=2
0, 0, 0, 5, 14, 28, 48, 75, 109, 143, 143, 0, 0, ... row n=3
0, 0, 0, 0, 14, 42, 90, 165, 274, 417, 560, 560, 0, ... row n=4
0, 0, 0, 0, 0, 42, 132, 297, 571, 988, 1548, 2108, 2108, 0, ... row n=5
...

Mathematica

t[0, k_ /; k <= 7] = 1; t[n_, k_] /; k < n || k > n+7 = 0; t[n_, k_] := t[n, k] = t[n-1, k] + t[n, k-1]; Table[t[n-k, k], {n, 0, 13}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 18 2013 *)

Crossrefs

Cf. Similar sequence: A216230, A216228, A216226, A216238, A216054, A217257.

Sequence in context: A220062 A216054 A217257 * A217593 A353434 A350529

Adjacent sequences: A217312 A217313 A217314 * A217316 A217317 A217318

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 17 2013

Status

approved