A156072 - OEIS

%I #12 Nov 26 2018 03:51:41

%S 1,1,1,1,0,1,1,0,0,1,1,1,1,1,1,1,1,2,2,1,1,1,1,2,3,2,1,1,1,2,3,4,4,3,

%T 2,1,1,3,5,6,6,6,5,3,1,1,4,7,9,9,9,9,7,4,1,1,6,10,13,14,14,14,13,10,6,

%U 1,1,9,15,19,21,22,22,21,19,15,9,1,1,13,22,28,31,33,34,33,31,28,22,13,1

%N T(n,k) = 1 + a(n) - a(k) - a(n - k), where a(n) = A078012(n+2), triangle read by rows (n >= 0, 0 <= k <= n).

%H G. C. Greubel, <a href="/A156072/b156072.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%e Triangle begins:

%e   1;

%e   1, 1;

%e   1, 0,  1;

%e   1, 0,  0,  1;

%e   1, 1,  1,  1,  1;

%e   1, 1,  2,  2,  1,  1;

%e   1, 1,  2,  3,  2,  1,  1;

%e   1, 2,  3,  4,  4,  3,  2,  1;

%e   1, 3,  5,  6,  6,  6,  5,  3,  1;

%e   1, 4,  7,  9,  9,  9,  9,  7,  4, 1;

%e   1, 6, 10, 13, 14, 14, 14, 13, 10, 6, 1;

%e   ...

%t Clear[a, t, n, m];

%t a[0] = 0; a[1] = 1; a[2] = 1;

%t a[n_] := a[n] = a[n - 1] + a[n - 3];

%t t[n_, m_] := 1 + a[n] - a[m] - a[n - m];

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%o (Maxima) (a[0] : 0, a[1] : 1, a[2] : 1, a[n] := a[n - 1] + a[n - 3], T(n,k) := 1 + a[n] - a[k] - a[n-k])$ create_list(T(n, k), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Nov 25 2018 */

%Y Cf. A000930, A156070, A176305, A176306, A176307, A176625, A176339, A176344.

%K nonn,tabl,easy

%O 0,18

%A _Roger L. Bagula_, Feb 03 2009

%E Edited and name clarified by _Franck Maminirina Ramaharo_, Nov 25 2018