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A216218 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=2, T(1,0) = T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1). 11

%I #7 Mar 14 2013 20:49:36

%S 1,1,1,0,2,0,0,2,2,0,0,0,4,0,0,0,0,4,4,0,0,0,0,0,8,0,0,0,0,0,0,8,8,0,

%T 0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,16,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,

%U 0,0,0,0

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

%C With zeros omitted, this is A173862.

%F T(n,n) = T(n+1,n) = T(n,n+1) = 2^n = A000079(n).

%F Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n+1) = A163403(n+1).

%e Square array begins:

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

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

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

%e 0, 0, 4, 8, 8, 0, 0, 0, ... row n=3

%e 0, 0, 0, 8, 16, 16, 0, 0, ... row n=4

%e 0, 0, 0, 0, 16, 32, 32, 0, ... row n=5

%e ...

%Y Cf. A000079, A016116, A216216, A216210, A068913

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 13 2013

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)