A173739 Square array read by antidiagonals (n >= 1, k >= 2): T(n,k) = b(n,k) + b(k-1,n+1), where b(n,k) = ((1 + sqrt(k))^n - (1 - sqrt(k))^n)/(2*sqrt(k)).

2, 3, 3, 6, 4, 6, 13, 8, 8, 13, 30, 18, 14, 18, 30, 71, 46, 28, 28, 46, 71, 170, 122, 70, 48, 70, 122, 170, 409, 330, 192, 108, 108, 192, 330, 409, 986, 898, 558, 288, 202, 288, 558, 898, 986, 2379, 2450, 1652, 868, 466, 466, 868, 1652, 2450, 2379, 5742, 6690, 4934, 2728, 1338, 880, 1338, 2728, 4934, 6690, 5742

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

Square array begins:
  n\k |   2   3    4    5    6    7     8     9 ...
  -------------------------------------------------
    1 |   2   3    6   13   30   71   170   409 ...
    2 |   3   4    8   18   46  122   330   898 ...
    3 |   6   8   14   28   70  192   558  1652 ...
    4 |  13  18   28   48  108  288   868  2728 ...
    5 |  30  46   70  108  202  466  1338  4264 ...
    6 |  71 122  192  288  466  880  2174  6560 ...
    7 | 170 330  558  868 1338 2174  4286 10888 ...
    8 | 409 898 1652 2728 4264 6560 10888 21760 ...
    ...

Mathematica

a[n_, q_] = ((1 + Sqrt[q])^n - (1 - Sqrt[q])^n)/(2*Sqrt[q]);
b = Table[Table[FullSimplify[ExpandAll[a[n, q]]], {n, 1, 11}], {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, q) := ((1 + sqrt(q))^n - (1 - sqrt(q))^n)/(2*sqrt(q))$
T(n, k) := b(n, k) + b(k - 1, n + 1)$
create_list(fullratsimp(T(k - 1, n - k + 3)), n, 1, 20, k, 2, n + 1);
/* Franck Maminirina Ramaharo, Jan 27 2019 */

Crossrefs

Cf. A173738.

Sequence in context: A238305 A337660 A049990 * A062774 A266286 A045892

Adjacent sequences: A173736 A173737 A173738 * A173740 A173741 A173742

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Feb 23 2010

Extensions

Edited by Franck Maminirina Ramaharo, Jan 27 2019

Status

approved