A061451 Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.

2, 3, 3, 4, 5, 5, 5, 7, 9, 8, 6, 9, 13, 17, 13, 7, 11, 17, 25, 31, 21, 8, 13, 21, 33, 49, 57, 34, 9, 15, 25, 41, 65, 94, 105, 55, 10, 17, 29, 49, 81, 129, 181, 193, 89, 11, 19, 33, 57, 97, 161, 253, 349, 355, 144, 12, 21, 37, 65, 113, 193, 321, 497, 673, 653, 233

Offset: 1

Author

Frank Ellermann, Jun 11 2001

Keywords

• nonn
• easy
• tabl
• nice

Examples

			2, 3, 5, 8 ... first order, a(1)=2, a(3)=3, a(6)=5, a(10)=8, ...
3, 5, 9,17 ... 2nd order, a(2)=3, a(5)=5, a(9)=9, ...
4, 7,13,25 ... 3rd order, a(4)=4, a(8)=7, ...
5, 9,17,33 ... 4th order, a(7)=5, ...
		

References

• N. Wirth, Algorithmen und Datenstrukturen, 1975, table 2.15 (ch. 2.3.4)

Links

• T. D. Noe, Rows n=1..50 of triangle, flattened

Crossrefs

Rows 1..6: A000045, A000213, A000288, A000322, A000383, A060455.

Programs

Mathematica

max = 12; Clear[f]; f[k_, n_] /; n > k := f[k, n] = Sum[f[k, n - j], {j, 1, k + 1}]; f[k_, n_] = 1; t = Table[ Table[ f[k, n], {n, k + 1, max}], {k, 1, max}]; Table[ t[[k - n + 1, n]], {k, 1, max - 1}, {n, 1, k}] // Flatten (* Jean-François Alcover, Apr 10 2013 *)