cp's OEIS Frontend

A217765 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=3 or if k-n >= 6, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).

%I A217765 #8 Mar 26 2013 13:23:13
%S A217765 1,1,1,1,2,1,1,3,3,0,1,4,6,3,0,1,5,10,9,0,0,0,6,15,19,9,0,0,0,6,21,34,
%T A217765 28,0,0,0,0,0,27,55,62,28,0,0,0,0,0,27,82,117,90,0,0,0,0,0,0,0,109,
%U A217765 199,207,90,0,0,0,0,0,0,0,109,308,406,297,0,0,0,0
%N A217765 Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=3 or if k-n >= 6, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = T(0,3) = T(0,4) = T(0,5) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
%C A217765 A hexagon arithmetic of E. Lucas.
%F A217765 T(n,n+4) = T(n,n+5) = A094829(n+2).
%F A217765 T(n,n+3) = A094834(n+1).
%F A217765 T(n,n+2) = A094833(n+1).
%F A217765 T(n,n+1) = A094832(n).
%F A217765 T(n,n) = A094831(n).
%F A217765 T(n+1,n) = T(n+2,n) = A094826(n).
%F A217765 sum(T(n-k,k), 0<=k<=n) = A065455(n).
%e A217765 Square array begins:
%e A217765 1, 1, 1, 1, 1, 1, 0, 0, 0, ... row n=0
%e A217765 1, 2, 3, 4, 5, 6, 6, 0, 0, ... row n=1
%e A217765 1, 3, 6, 10, 15, 21, 27, 27, 0, 0, ... row n=2
%e A217765 0, 3, 9, 19, 34, 55, 82, 109, 109, 0, 0, ... row n=3
%e A217765 0, 0, 9, 28, 62, 117, 199, 308, 417, 417, 0, 0, ... row n=4
%e A217765 0, 0, 0, 28, 90, 207, 406, 714, 1131, 1548, 1548, 0, 0, ... row n=5
%e A217765 ...
%e A217765 Square array, read by rows, with 0 omitted:
%e A217765 1, 1, 1, 1, 1, 1
%e A217765 1, 2, 3, 4, 5, 6, 6
%e A217765 1, 3, 6, 10, 15, 21, 27, 27
%e A217765 3, 9, 19, 34, 55, 82, 109, 109
%e A217765 9, 28, 62, 117, 199, 308, 417, 417
%e A217765 28, 90, 207, 406, 714, 1131, 1548, 1548
%e A217765 90, 297, 703, 1417, 2548, 4096, 5644, 5644
%e A217765 297, 1000, 2417, 4965, 9061, 14705, 20349, 20349
%e A217765 1000, 3417, 8382, 17443, 32148, 52497, 72846, 72846
%e A217765 3417, 11799, 29242, 61390, 113887, 186733, 259579, 259579
%e A217765 11799, 41041, 102431, 216318, 403051, 662630, 922209, 922209
%e A217765 ...
%Y A217765 Cf. Similar sequences: A216201, A216210, A216216, A216218, ...
%K A217765 nonn,tabl
%O A217765 0,5
%A A217765 _Philippe Deléham_, Mar 24 2013