OFFSET
1,2
COMMENTS
Form the square array in which row m satisfies r(0) = r(1) = 1; r(n) = m*r(n-1) + r(n-2):
1 1 2 3 5 8 13 21 ...
1 1 3 7 17 41 99 ...
1 1 4 13 43 142 ...
1 1 5 21 89 377 ...
...
Now form a triangle by taking the first k terms of column k:
1
2, 3
3, 7, 13
5, 17, 43, 89
8, 41, 142, 377, 836
...
MATHEMATICA
f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == m*a[n - 1] + a[n - 2], a[0] == 1, a[1] == 1}, a[n], n][[1]] // FullSimplify] a = Table[Table[Rationalize[N[f[n], 100], 0], {m, 1, n}], {n, 1, 10}] Flatten[a]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 09 2006
EXTENSIONS
Edited by N. J. A. Sloane, Mar 02 2008
STATUS
approved