A104793 Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.

1, 5, 1, 13, 5, 1, 28, 13, 5, 1, 54, 28, 13, 5, 1, 98, 54, 28, 13, 5, 1, 171, 98, 54, 28, 13, 5, 1, 291, 171, 98, 54, 28, 13, 5, 1, 487, 291, 171, 98, 54, 28, 13, 5, 1, 806, 487, 291, 171, 98, 54, 28, 13, 5, 1, 1324, 806, 487, 291, 171, 98, 54, 28, 13, 5, 1

Offset: 1

Author

Gary W. Adamson, Mar 26 2005

Keywords

• nonn
• tabl

Comments

Repeatedly writing the sequence A023537 backwards.

Examples

			First few rows of the triangle are:
   1;
   5,  1;
  13,  5,  1;
  28, 13,  5,  1;
  54, 28, 13,  5, 1;
  98, 54, 28, 13, 5, 1; ...
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Row sums are in A027963.

Cf. A104765.

Programs

GAP

Flat(List([1..12], n-> List([0..n-1], k-> Lucas(1, -1, n-k+4)[2] -3*n+3*k-7 ))); # G. C. Greubel, Jun 01 2019

Magma

[[Lucas(n-k+4) -(3*n-3*k+7): k in [0..n-1]]: n in [1..12]]; // G. C. Greubel, Jun 01 2019

Mathematica

Table[LucasL[n-k+4] -3*n+3*k-7, {n,1,12}, {k,0,n-1}]//Flatten (* G. C. Greubel, Jun 01 2019 *)

PARI

{T(n,k) = fibonacci(n-k+5) + fibonacci(n-k+3) -3*n +3*k - 7}; \\ G. C. Greubel, Jun 01 2019

Sage

[[lucas_number2(n-k+4, 1, -1) -3*n+3*k-7 for k in (0..n-1)] for n in (1..12)] # G. C. Greubel, Jun 01 2019

Formula

From Ralf Stephan, Apr 05 2009: (Start)

T(n,k) = Lucas(n-k+4) - (3*n - 3*k + 7).

T(n,k) = A023537(A004736(n, k+1)). (End)

Extensions

Edited by Ralf Stephan, Apr 05 2009