A058294 Successive rows of a triangle, the columns of which are generalized Fibonacci sequences S(j).

1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 7, 10, 7, 3, 1, 1, 4, 13, 30, 43, 30, 13, 4, 1, 1, 5, 21, 68, 157, 225, 157, 68, 21, 5, 1, 1, 6, 31, 130, 421, 972, 1393, 972, 421, 130, 31, 6, 1, 1, 7, 43, 222, 931, 3015, 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1

Offset: 1

Author

Russell Walsmith, Dec 07 2000

Keywords

• nonn
• tabf
• nice
• easy

Comments

From Reinhard Zumkeller, Sep 14 2014: (Start)

T(n,k) = A102473(n,k), k=1..n;

T(n,k) = A102472(n,k-n+1), k=n..2*n-1;

T(n,n) = A001040(n). (End)

Examples

			Triangle begins:
  1;
  1, 1, 1;
  1, 2, 3,  2, 1;
  1, 3, 7, 10, 7, 3, 1;
  ...
		

Links

• Reinhard Zumkeller, >Rows n = 1..125 of table, flattened
• Russell Walsmith, CL-Chemy Transforms Fibonacci-Type Sequences to Arrays

Crossrefs

A001040, A001053, A058307, A058308, A058309 are columns of this triangle.

Cf. A102472, A102473.

Programs

Haskell

a058294 n k = a058294_tabf !! (n-1) !! (k-1)
a058294_row n = a058294_tabf !! (n-1)
a058294_tabf = [1] : zipWith (++) xss (map (tail . reverse) xss)
               where xss = tail a102473_tabl
-- Reinhard Zumkeller, Sep 14 2014

Mathematica

t[n_, n_] = 1; t[n_, k_] := t[n, k] = If[nJean-François Alcover, Oct 05 2016 *)

Formula

The j-th column S(j) is generated by a(n+1) = (n+j)*a(n) + a(n-1), a(0)=0, a(1)=1.