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A156072 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).

%I A156072 #12 Nov 26 2018 03:51:41
%S A156072 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 A156072 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 A156072 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 A156072 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 A156072 G. C. Greubel, <a href="/A156072/b156072.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e A156072 Triangle begins:
%e A156072   1;
%e A156072   1, 1;
%e A156072   1, 0,  1;
%e A156072   1, 0,  0,  1;
%e A156072   1, 1,  1,  1,  1;
%e A156072   1, 1,  2,  2,  1,  1;
%e A156072   1, 1,  2,  3,  2,  1,  1;
%e A156072   1, 2,  3,  4,  4,  3,  2,  1;
%e A156072   1, 3,  5,  6,  6,  6,  5,  3,  1;
%e A156072   1, 4,  7,  9,  9,  9,  9,  7,  4, 1;
%e A156072   1, 6, 10, 13, 14, 14, 14, 13, 10, 6, 1;
%e A156072   ...
%t A156072 Clear[a, t, n, m];
%t A156072 a[0] = 0; a[1] = 1; a[2] = 1;
%t A156072 a[n_] := a[n] = a[n - 1] + a[n - 3];
%t A156072 t[n_, m_] := 1 + a[n] - a[m] - a[n - m];
%t A156072 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A156072 Flatten[%]
%o A156072 (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 A156072 Cf. A000930, A156070, A176305, A176306, A176307, A176625, A176339, A176344.
%K A156072 nonn,tabl,easy
%O A156072 0,18
%A A156072 _Roger L. Bagula_, Feb 03 2009
%E A156072 Edited and name clarified by _Franck Maminirina Ramaharo_, Nov 25 2018