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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).
3
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, 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, 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
OFFSET
0,18
EXAMPLE
Triangle begins:
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, 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, 1;
...
MATHEMATICA
Clear[a, t, n, m];
a[0] = 0; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 3];
t[n_, m_] := 1 + a[n] - a[m] - a[n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
PROG
(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 */
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Feb 03 2009
EXTENSIONS
Edited and name clarified by Franck Maminirina Ramaharo, Nov 25 2018
STATUS
approved