A104796 Triangle read by rows: T(n,k) = (n+1-k)*Fibonacci(n+2-k), for n>=1, 1<=k<=n.

1, 4, 1, 9, 4, 1, 20, 9, 4, 1, 40, 20, 9, 4, 1, 78, 40, 20, 9, 4, 1, 147, 78, 40, 20, 9, 4, 1, 272, 147, 78, 40, 20, 9, 4, 1, 495, 272, 147, 78, 40, 20, 9, 4, 1, 890, 495, 272, 147, 78, 40, 20, 9, 4, 1, 1584, 890, 495, 272, 147, 78, 40, 20, 9, 4, 1, 2796, 1584, 890, 495, 272

Offset: 1

Author

Gary W. Adamson, Mar 26 2005

Keywords

• nonn
• tabl

Comments

The first column is A023607 (without the leading zero).

Examples

			Rows 1,2,3,4,5,6 and columns 1,2,3,4,5,6 of the triangle are:
1;
4, 1;
9, 4, 1;
20, 9, 4, 1;
40, 20, 9, 4, 1;
78, 40, 20, 9, 4, 1;
...
Row 3 for example is 3*F(4), 2*F(3), 1*F(2) = 3*3, 2*2, 1*1 = 9, 4, 1.
Row 4 is 4*F(5), 3*F(4), 2*F(3), 1*F(2) = 4*5, 3*3, 2*2, 1*1 = 20, 9, 4, 1.
Reading the rows backwards gives an initial segment of the terms of A023607 (but without the initial zero).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Row sums are in A094584.

Cf. A023607, A104762, A104765, A000045.

Programs

Mathematica

Table[(n+1-k)Fibonacci[n+2-k],{n,20},{k,n}]//Flatten (* Harvey P. Dale, Sep 24 2020 *)
Module[{nn=20,c},c=LinearRecurrence[{2,1,-2,-1},{1,4,9,20},nn];Table[ Reverse[ Take[c,n]],{n,nn}]]//Flatten (* Harvey P. Dale, Sep 25 2020 *)

Extensions

Edited by Ralf Stephan, Apr 05 2009

Entry revised by N. J. A. Sloane, Sep 23 2020