cp's OEIS Frontend

A214846 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 6 or if k-n >= 6, T(k,0) = T(0,k) = 1 if 0 <= k <= 5, T(n,k) = T(n-1,k) + T(n,k-1).

%I A214846 #29 Nov 18 2018 09:55:01
%S A214846 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,0,6,15,20,15,6,0,0,6,21,
%T A214846 35,35,21,6,0,0,0,27,56,70,56,27,0,0,0,0,27,83,126,126,83,27,0,0,0,0,
%U A214846 0,110,209,252,209,110,0,0,0,0,0,0,110,319,461,461,319,110,0,0,0,0,0,0,0,429,780,922,780,429,0,0,0,0
%N A214846 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >= 6 or if k-n >= 6, T(k,0) = T(0,k) = 1 if 0 <= k <= 5, T(n,k) = T(n-1,k) + T(n,k-1).
%C A214846 An arithmetic hexagon of E. Lucas.
%H A214846 E. Lucas, <a href="https://archive.org/details/thoriedesnombre00lucagoog/page/n119">Théorie des nombres</a>, Gauthier-Villars, Paris 1891, Tome 1, p. 89.
%F A214846 T(n,n) = A087944(n).
%F A214846 T(n,n+1) = T(n+1,n) = A087946(n).
%F A214846 T(n+2,n) = T(n,n+2) = A001353(n+1).
%F A214846 T(n+3,n) = T(n,n+3) = A216271(n).
%F A214846 T(n+5,n) = T(n+4,n) = T(n,n+4) = T(n,n+5) = A216263(n).
%F A214846 Sum_{k=0..n} T(n-k,k) = A216241(n).
%e A214846 Square array begins:
%e A214846   1, 1,  1,   1,   1,   1,    0,    0,    0,     0,     0, ...
%e A214846   1, 2,  3,   4,   5,   6,    6,    0,    0,     0,     0, ...
%e A214846   1, 3,  6,  10,  15,  21,   27,   27,    0,     0,     0, ...
%e A214846   1, 4, 10,  20,  35,  56,   83,  110,  110,     0,     0, ...
%e A214846   1, 5, 15,  35,  70, 126,  209,  319,  429,   429,     0, ...
%e A214846   1, 6, 21,  56, 126, 252,  461,  780, 1209,  1638,  1638, ...
%e A214846   0, 6, 27,  83, 209, 461,  922, 1702, 2911,  4549,  6187, ...
%e A214846   0, 0, 27, 110, 319, 780, 1702, 3404, 6315, 10864, 17051, ...
%e A214846   ...
%Y A214846 Cf. similar sequences: A000007, A216218, A216216, A216210, A216219.
%K A214846 nonn,tabl
%O A214846 0,5
%A A214846 _Philippe Deléham_, Mar 16 2013