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A217593 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=1 or if k-n >= 9, T(0,k) = 1 for k = 0..8, T(n,k) = T(n-1,k) + T(n,k-1). 3
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, 1, 7, 20, 28, 14, 0, 0, 0, 0, 0, 8, 27, 48, 42, 0, 0, 0, 0, 0, 0, 8, 35, 75, 90, 42, 0, 0, 0, 0, 0, 0, 0, 43, 110, 165, 132, 0, 0, 0, 0, 0, 0, 0, 0, 43, 153, 275, 297, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 428, 572, 429, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

REFERENCES

A hexagon arithmetic of E. Lucas.

LINKS

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

FORMULA

T(n,n)   = A033191(n).

T(n,n+1) = A033191(n+1).

T(n,n+2) = A033190(n+1).

T(n,n+3) = A094667(n+1).

T(n,n+4) = A093131(n+1) = A030191(n).

T(n,n+5) = A094788(n+2).

T(n,n+6) = A094825(n+3).

T(n,n+7) = T(n,n+8) = A094865(n+3).

Sum_{k, 0<=k<=n} T(n-k,k) = A178381(n).

EXAMPLE

Square array begins :

1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, ...

0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 0, ...

0, 0, 2, 5, 9, 14, 20, 27, 35, 43, 43, 0, 0, ...

0, 0, 0, 5, 14, 28, 75, 110, 153, 196, 196, 0, 0, ....

0, 0, 0, 0, 14, 42, 90, 165, 275, 428, 624, 820, 820, 0, 0, ...

...

Square array, read by rows, with 0 omitted:

1, 1, 1, 1, 1, 1, 1, 1, 1

1, 2, 3, 4, 5, 6, 7, 8, 8

2, 5, 9, 14, 20, 27, 35, 43, 43

5, 14, 28, 48, 75, 110, 153, 196, 196

14, 42, 90, 165, 275, 428, 624, 820, 820

42, 132, 297, 572, 1000, 1624, 2444, 3264, 3264

132, 429, 1001, 2001, 3625, 6069, 9333, 12597, 12597

429, 1430, 3431, 7056, 13125, 22458, 35055, 47652, 47652

...

CROSSREFS

Sequence in context: A216054 A217257 A217315 * A322279 A292861 A292133

Adjacent sequences:  A217590 A217591 A217592 * A217594 A217595 A217596

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 18 2013

STATUS

approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)