login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Square array T read by antidiagonals: T(n,k) = 0 if n-k>=4 or if k-n>=4, T(3,0) = T(2,0) = TT(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).
12

%I #7 Mar 13 2013 13:30:44

%S 1,1,1,1,2,1,1,3,3,1,0,4,6,4,0,0,4,10,10,4,0,0,0,14,20,14,0,0,0,0,14,

%T 34,34,14,0,0,0,0,0,48,68,48,0,0,0,0,0,0,48,116,116,48,0,0,0,0,0,0,0,

%U 164,232,164,0,0,0,0

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

%F T(n,n) = A006012(n).

%F T(n,n+1) = T(n+1,n) = A007052(n).

%F T(n,n+2) = T(n,n+3) = T(n+2,n) = T(n+3,n) = A007070(n).

%F Sum_{k, 0<=k<=n} T(n-k,k) = A068912(n).

%e Square array begins:

%e 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ... row n=0

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

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

%e 1, 4, 10, 20, 34, 48, 48, 0, 0, 0, ... row n=3

%e 0, 4, 14, 34, 68, 116, 164, 164, 0, 0, ... row n=4

%e 0, 0, 14, 48, 116, 232, 396, 560, 560, 0, ... row n=5

%e 0, 0, 0, 48, 164, 396, 792, 1352, 1912, 1912, row n=6

%e ...

%Y Cf. A006012, A007052, A007070, A068912

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 12 2013