A173738 Square array read by antidiagonals (n >= 0, k >= 2): T(n,k) = b(n,k) + b(k-2,n+2), where b(n,k) = ((1 + sqrt(k))^n + (1 - sqrt(k))^n)/2.

2, 2, 2, 4, 2, 4, 8, 5, 5, 8, 18, 11, 10, 11, 18, 42, 29, 19, 19, 29, 42, 100, 77, 48, 32, 48, 77, 100, 240, 209, 129, 75, 75, 129, 209, 240, 578, 569, 374, 198, 146, 198, 374, 569, 578, 1394, 1553, 1103, 601, 333, 333, 601, 1103, 1553, 1394, 3364, 4241, 3292, 1884, 960, 632, 960, 1884, 3292, 4241, 3364

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

Cf. A173739.

Sequence in context: A342457 A286849 A098069 * A135838 A279966 A349483

Adjacent sequences: A173735 A173736 A173737 * A173739 A173740 A173741

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Feb 23 2010

Extensions

Edited by Franck Maminirina Ramaharo, Jan 27 2019

Status

approved