A121875 Triangular array read by rows: see Comments for definition.

1, 2, 3, 3, 7, 13, 5, 17, 43, 89, 8, 41, 142, 377, 836, 13, 99, 469, 1597, 4341, 10063, 21, 239, 1549, 6765, 22541, 62011, 148149, 34, 577, 5116, 28657, 117046, 382129, 1057792, 2581921, 55, 1393, 16897, 121393, 607771, 2354785, 7552693, 20973217

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 09 2006

Keywords

• nonn
• tabl

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

...

Crossrefs

Cf. A135597.

Programs

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]

Extensions

Edited by N. J. A. Sloane, Mar 02 2008