cp's OEIS Frontend

A216228 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=3, T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%I A216228 #16 Mar 17 2013 04:18:51
%S A216228 1,1,0,1,1,0,0,2,0,0,0,2,2,0,0,0,0,4,0,0,0,0,0,4,4,0,0,0,0,0,0,8,0,0,
%T A216228 0,0,0,0,0,8,8,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,16,0,0,0,0,0,0,
%U A216228 0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,32,32
%N A216228 Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=3, T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C A216228 An arithmetic hexagon of E. Lucas.
%D A216228 E. Lucas, Théorie des nombres, Albert Blanchard, Paris 1958, Tome 1, p.89
%H A216228 E. Lucas, <a href="http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&amp;O=NUMM-29021">Théorie des nombres</a>, Tome 1, Jacques Gabay, Paris, 1991, p.89
%F A216228 T(n,n) = A011782(n).
%F A216228 T(n,n+1) = T(n,n+2) = 2^n = A000079(n).
%F A216228 Sum_{k, 0<=k<=n} T(n-k,k) = A016116(n).
%F A216228 Sum_{n, n>=0} T(n,k) = A084215(k).
%F A216228 Sum_{k, k>=0} T(n,k) = A084215(n+1), n>=1.
%e A216228 Square array begins:
%e A216228 1, 1, 1, 0, 0,  0,  0,  0, ... row n=0
%e A216228 0, 1, 2, 2, 0,  0,  0,  0, ... row n=1
%e A216228 0, 0, 2, 4, 4,  0,  0,  0, ... row n=2
%e A216228 0, 0, 0, 4, 8,  8,  0,  0, ... row n=3
%e A216228 0, 0, 0, 0, 8, 16, 16,  0, ... row n=4
%e A216228 0, 0, 0, 0, 0, 16, 32, 32, ... row n=5
%e A216228 ...
%Y A216228 Cf. A000079, A011782, A016116, A068914, A084215.
%K A216228 nonn,tabl
%O A216228 0,8
%A A216228 _Philippe Deléham_, Mar 13 2013