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

1,2

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

...

Links

Table of n, a(n) for n=1..44.

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

Cf. A135597.

Sequence in context: A169653 A129012 A136122 * A036251 A176022 A316275

Adjacent sequences: A121872 A121873 A121874 * A121876 A121877 A121878

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