A216054 - OEIS

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A216054

Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 1 or if k-n >= 6, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, 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, 0, 5, 9, 5, 0, 0, 0, 0, 5, 14, 14, 0, 0, 0, 0, 0, 0, 19, 28, 14, 0, 0, 0, 0, 0, 0, 19, 47, 42, 0, 0, 0, 0, 0, 0, 0, 0, 66, 89, 42, 0, 0, 0, 0, 0, 0, 0, 0, 66, 155, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 286, 131, 0, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

COMMENTS

A hexagon arithmetic of E. Lucas.

REFERENCES

E. Lucas, Théorie des nombres, A.Blanchard, Paris, 1958, Tome 1, p.89

LINKS

Table of n, a(n) for n=0..86.

FORMULA

T(n,n) = A080937(n).

T(n,n+1) = A080937(n+1).

T(n,n+2) = A094790(n+1).

T(n,n+3) = A094789(n+1).

T(n,n4) = T(n,n+5) = A005021(n).

Sum_{k, 0<=k<=n} T(n-k,k) = A028495(n).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=0

0, 1, 2, 3, 4, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... row n=1

0, 0, 2, 5, 9, 14, 19, 19, 0, 0, 0, 0, 0, 0, 0, ... row n=2

0, 0, 0, 5, 14, 28, 47, 66, 66, 0, 0, 0, 0, 0, 0, ... row n=3

0, 0, 0, 0, 14, 42, 89, 155, 221, 221, 0, 0, 0, 0, ... row n=4

0, 0, 0, 0, 0, 0, 42, 131, 286, 507, 728, 728, 0, 0, ... row n=5

0, 0, 0, 0, 0, 0, 131, 417, 924, 1652, 2380, 2380, 0, ... row n=6

...

MATHEMATICA

Clear[t]; t[0, k_ /; k <= 5] = 1; t[n_, k_] /; k < n || k > n+5 = 0; t[n_, k_] := t[n, k] = t[n-1, k] + t[n, k-1]; Table[t[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 18 2013 *)

CROSSREFS

Cf. A006053, A052547, A096976, A187066,

Cf. Similar sequences A216230, A216228, A216226, A216238

Sequence in context: A216238 A157608 A220062 * A217257 A217315 A217593

Adjacent sequences: A216051 A216052 A216053 * A216055 A216056 A216057

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 16 2013

STATUS

approved