OFFSET
0,1
LINKS
G. C. Greubel, Antidiagonals n = 0..50, flattened
EXAMPLE
Square array begins:
n\k | 2 3 4 5 6 7 8 9 ...
------------------------------------------------
0 | 2 2 4 8 18 42 100 240 ...
1 | 2 2 5 11 29 77 209 569 ...
2 | 4 5 10 19 48 129 374 1103 ...
3 | 8 11 19 32 75 198 601 1884 ...
4 | 18 29 48 75 146 333 960 3035 ...
5 | 42 77 129 198 333 632 1585 4760 ...
6 | 100 209 374 601 960 1585 3186 8073 ...
7 | 240 569 1103 1884 3035 4760 8073 16256 ...
...
MATHEMATICA
a[n_, q_] = ((1 + Sqrt[q])^n + (1 - Sqrt[q])^n)/2;
b = Table[Table[FullSimplify[ExpandAll[a[n, q]]], {n, 0, 10}], {q, 2, 12}];
c = (b + Transpose[b]);
Table[Table[c[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}] // Flatten
PROG
(Maxima)
b(n, k) := ((1 + sqrt(k))^n + (1 - sqrt(k))^n)/2$
T(n, k) := b(n, k) + b(k - 2, n + 2)$
create_list(fullratsimp(T(k - 2, n - k + 4)), n, 0, 20, k, 2, n + 2);
/* Franck Maminirina Ramaharo, Jan 27 2019 */
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Feb 23 2010
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 27 2019
STATUS
approved