A217593 - OEIS

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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).

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 * A353434 A350529 A322279

Adjacent sequences: A217590 A217591 A217592 * A217594 A217595 A217596

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 18 2013

STATUS

approved