A158753 Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.

1, 4, 1, 11, 4, 1, 29, 11, 4, 1, 76, 29, 11, 4, 1, 199, 76, 29, 11, 4, 1, 521, 199, 76, 29, 11, 4, 1, 1364, 521, 199, 76, 29, 11, 4, 1, 3571, 1364, 521, 199, 76, 29, 11, 4, 1, 9349, 3571, 1364, 521, 199, 76, 29, 11, 4, 1, 24476, 9349, 3571, 1364, 521, 199, 76, 29, 11, 4, 1

Offset

2,2

References

H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp. 159-162.

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k) = 5*e(n, k), where e(n,k) = (e(n-1, k)*e(n, k-1) + 1)/e(n-1, k-1), and e(n, 0) = GoldenRatio^(n) + GoldenRatio^(-n).

Sum_{k=0..n} T(n, k) = A004146(n-1).

T(n, k) = A000032(2*(n-k) + 1). - G. C. Greubel, Dec 06 2021

Example

Triangle begins as:
     1;
     4,   1;
    11,   4,   1;
    29,  11,   4,  1;
    76,  29,  11,  4,  1;
   199,  76,  29, 11,  4,  1;
   521, 199,  76, 29, 11,  4,  1;
  1364, 521, 199, 76, 29, 11,  4,  1;

Mathematica

Table[LucasL[2*(n-k) + 1], {n, 2, 16}, {k, 2, n}]//Flatten (* G. C. Greubel, Dec 06 2021 *)

Prog

(Magma) [Lucas(2*n-2*k+1): k in [2..n], n in [2..16]]; // G. C. Greubel, Dec 06 2021
(Sage) flatten([[lucas_number2(2*(n-k)+1, 1, -1) for k in (2..n)] for n in (2..16)]) # G. C. Greubel, Dec 06 2021

Crossrefs

Cf. A000032, A002878, A004146, A158786.

Sequence in context: A178519 A094503 A113897 * A183884 A135552 A181690

Adjacent sequences: A158750 A158751 A158752 * A158754 A158755 A158756

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Mar 25 2009

Extensions

Edited by G. C. Greubel, Dec 06 2021

Status

approved