A216201 - OEIS

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A216201

Square array T, read by antidiagonals : T(n,k) = 0 if n-k>=3 or if k-n>=4, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

1, 1, 1, 1, 2, 1, 1, 3, 3, 0, 0, 4, 6, 3, 0, 0, 4, 10, 9, 0, 0, 0, 0, 14, 19, 9, 0, 0, 0, 0, 14, 33, 28, 0, 0, 0, 0, 0, 0, 47, 61, 28, 0, 0, 0, 0, 0, 0, 47, 108, 89, 0, 0, 0, 0, 0, 0, 0, 0, 155, 197, 89, 0, 0, 0, 0

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

OFFSET

0,5

REFERENCES

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

LINKS

Table of n, a(n) for n=0..65.

E. Lucas, Théorie des nombres, Tome 1, Jacques Gabay, Paris, 1991, p.89

FORMULA

T(n,n) = A052975(n).

T(n,n+1) = A060557(n).

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

T(n,n+2) = T(n,n+3) = A094789(n+1).

Sum_{k, 0<=k<=n} T(n-k,k) = (-1)^n*A078038(n).

EXAMPLE

Square array begins:

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

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

1, 3, 6, 10, 14, 14, 0, 0, 0, 0, 0, 0, 0, ... row n = 2

0, 3, 9, 19, 33, 47, 47, 0, 0, 0, 0, 0, 0, ... row n = 3

0, 0, 9, 28, 61, 108, 155, 155, 0, 0, 0, 0, 0, ... row n = 4

0, 0, 0, 28, 89, 197, 352, 507, 507, 0, 0, 0, 0, ... row n = 5

0, 0, 0, 0, 89, 286, 638,1147,1652,1652, 0, 0, 0, ... row n = 6

...

CROSSREFS

Cf. A052975, A060557, A078038, A095789, A094790

Sequence in context: A122044 A120744 A053423 * A127514 A078802 A216232

Adjacent sequences: A216198 A216199 A216200 * A216202 A216203 A216204

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 12 2013

STATUS

approved