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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)).
1
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
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 A372808 A266286
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, Feb 23 2010
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 27 2019
STATUS
approved