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

1,2

Comments

Repeatedly writing the sequence A023537 backwards.

Links

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

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)

Example

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; ...

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 *)

Prog

(PARI) {T(n, k) = fibonacci(n-k+5) + fibonacci(n-k+3) -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
(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
(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

Crossrefs

Row sums are in A027963.

Cf. A104765.

Sequence in context: A327766 A147348 A081224 * A243883 A147004 A319664

Adjacent sequences: A104790 A104791 A104792 * A104794 A104795 A104796

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 26 2005

Extensions

Edited by Ralf Stephan, Apr 05 2009

Status

approved