A217770 - OEIS

%I #16 Apr 05 2013 12:27:01

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,0,1,5,10,10,4,0,0,6,15,20,14,0,0,0,6,21,

%T 35,34,14,0,0,0,0,27,56,69,48,0,0,0,0,0,27,83,125,117,48,0,0,0,0,0,0,

%U 110,208,242,165,0,0,0,0,0,0,0,110,318,450,407,165

%N Square array T, read by antidiagonals: T(n,k) = 0 if n-k >=4 or if k-n >= 6, T(3,0) = 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 A hexagon arithmetic of E. Lucas.

%F T(n,n+4) = T(n,n+5) = A094788(n+2).

%F T(n,n+3) = A217783(n).

%F T(n,n+2) = A217779(n).

%F T(n,n+1) = A081567(n).

%F T(n,n)   = A217782(n).

%F T(n+1,n) = A217778(n).

%F T(n+3,n) = T(n+2,n) = A094667(n+1).

%F Sum(T(n-k,k), k=0..n) = A217777(n).

%e Square array begins:

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

%e n=1: 1, 2,  3,  4,   5,   6,   6,   0,    0,    0,    0, 0, ...

%e n=2: 1, 3,  6, 10,  15,  21,  27,  27,    0,    0,    0, 0, ...

%e n=3: 1, 4, 10, 20,  35,  56,  83, 110,  110,    0,    0, 0, ...

%e n=4: 0, 4, 14, 34,  69, 125, 208, 318,  428,  428,    0, 0, ...

%e n=5: 0, 0, 14, 48, 117, 242, 450, 768, 1196, 1624, 1624, 0, ...

%e ...

%e Square array, read by rows, with 0 omitted:

%e ...1,    1,     1,     1,     1,      1

%e ...1,    2,     3,     4,     5,      6,      6

%e ...1,    3,     6,    10,    15,     21,     27,     27

%e ...1,    4,    10,    20,    35,     56,     83,    110,    110

%e ...4,   14,    34,    69,   125,    208,    318,    428,    428

%e ..14,   48,   117,   242,   450,    768,   1196,   1624,   1624

%e ..48,  165,   407,   857,  1625,   2821,   4445,   6069,   6069

%e .165,  572,  1429,  3054,  5875,  10320,  16389,  22458,  22458

%e .572, 2001,  5055, 10930, 21250,  37639,  60097,  82555,  82555

%e 2001, 7056, 17986, 39236, 76875, 136972, 219527, 302082, 302082

%e ...

%e Triangle begins:

%e 1

%e 1, 1

%e 1, 2,  1

%e 1, 3,  3,  1

%e 1, 4,  6,  4,  0

%e 1, 5, 10, 10,  4,  0

%e 0, 6, 15, 20, 14,  0, 0

%e 0, 6, 21, 35, 34, 14, 0, 0

%e ...

%Y Cf. Similar sequences: A214846, A216054, A216201, A216210, A216216, A216218, A216219, A216220, A216226, A216228, A216229, A216230, A216232, A216235, A216236, A216238, A217257, A217315, A217593, A217765.

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 24 2013