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A216235 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 2 or if k-n >= 5, T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1). 4
1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 1, 4, 5, 0, 0, 0, 5, 9, 5, 0, 0, 0, 5, 14, 14, 0, 0, 0, 0, 0, 19, 28, 14, 0, 0, 0, 0, 0, 19, 47, 42, 0, 0, 0, 0, 0, 0, 0, 66, 89, 42, 0, 0, 0, 0, 0, 0, 0, 66, 155, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 286, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 221, 507, 417, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Arithmetic hexagon of E. Lucas.

LINKS

Table of n, a(n) for n=0..90.

E. Lucas, Théorie des nombres, Gauthier-Villars, Paris 1891, Tome 1, p. 89.

FORMULA

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

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

T(n,n+2) = A094789(n+1).

T(n,n+3) = T(n,n+4) = A005021(n).

Sum_{k=0..n} T(n-k,k) = A028495(n+1). - Philippe Deléham, Mar 23 2013

EXAMPLE

Square array begins:

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

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

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

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

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

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

  ...

CROSSREFS

Cf. A005021, A080937, A094789, A094790.

Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232.

Sequence in context: A197707 A253668 A216220 * A306914 A317023 A319284

Adjacent sequences:  A216232 A216233 A216234 * A216236 A216237 A216238

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 14 2013

STATUS

approved

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Last modified May 19 13:18 EDT 2019. Contains 323393 sequences. (Running on oeis4.)