A217593 - OEIS

%I #11 Mar 28 2013 20:23:16

%S 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,

%T 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,

%U 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

%N 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).

%D A hexagon arithmetic of E. Lucas.

%F T(n,n)   = A033191(n).

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

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

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

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

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

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

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

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

%e Square array begins :

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, ...

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

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

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

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

%e ...

%e Square array, read by rows, with 0 omitted:

%e 1, 1, 1, 1, 1, 1, 1, 1, 1

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

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

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

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

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

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

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

%e ...

%K nonn,tabl

%O 0,8

%A _Philippe Deléham_, Mar 18 2013