|
%I #16 Mar 19 2013 07:03:19
%S 1,1,0,1,1,0,1,2,0,0,1,3,2,0,0,0,4,5,0,0,0,0,4,9,5,0,0,0,0,0,13,14,0,
%T 0,0,0,0,0,13,27,14,0,0,0,0,0,0,0,40,41,0,0,0,0,0,0,0,0,40,81,41,0,0,
%U 0,0,0,0,0,0,0,121,122,0,0,0,0,0,0
%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=5, T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C Hexagon arithmetic of E. Lucas.
%D E. Lucas, Théorie des nombres, Albert Blanchard, Paris, 1958, Tome1, p.89
%H E. Lucas, <a href="http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-29021">Théorie des nombres</a>, Tome 1, Jacques Gabay, Paris, 1991, p.89
%F T(n,n) = A124302(n).
%F T(n,n+1) = A124302(n+1).
%F T(n,n+2) = 3^n = A000244(n).
%F T(n,n+3) = T(n,n+4) = A003462(n+1).
%F Sum_{k, 0<=k<=n} T(n-k,k) = A182522(n).
%e Square array begins:
%e 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ... row n=0
%e 0, 1, 2, 3, 4, 4, 0, 0, 0, 0, 0, ... row n=1
%e 0, 0, 2, 5, 9, 13, 13, 0, 0, 0, 0, ... row n=2
%e 0, 0, 0, 5, 14, 27, 40, 40, 0, 0, 0, ... row n=3
%e 0, 0, 0, 0, 14, 41, 81, 121, 121, 0, 0, ... row n=4
%e 0, 0, 0, 0, 0, 41, 122, 243, 364, 364, 0, ... row n=5
%e 0, 0, 0, 0, 0, 0, 122, 365, 729, 1093, 1093, ... row n=6
%e ...
%Y Cf. A000244, A003462, A124302, A182522.
%Y Similar sequences: A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236.
%K nonn,tabl
%O 0,8
%A _Philippe Deléham_, Mar 14 2013
|
