A140895 A Lucas-Binet triangle read by rows: t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2.

1, 1, 4, 1, 6, 16, 1, 8, 22, 92, 1, 12, 34, 188, 716, 1, 14, 40, 248, 976, 4928, 1, 18, 52, 392, 1616, 9504, 44864, 1, 20, 58, 476, 1996, 12560, 61048, 348176, 1, 24, 70, 668, 2876, 20448, 104168, 658192, 3608080, 1, 30, 88, 1016, 4496, 37440, 200768

Offset

1,3

Comments

Row sums are: {1, 5, 23, 123, 951, 6207, 56447, 424335, 4394527, 67853311, ...}.

References

Arthur Benjamin and Jennifer J. Quinn, Fibonacci and Lucas Identities through Colored Tilings, Utilitas Mathematica, Vol 56, pp. 137-142, November, 1999. http://www.math.hmc.edu/~benjamin/papers.html

Links

Table of n, a(n) for n=1..52.

Formula

t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2.

Example

{1},
{1, 4},
{1, 6, 16},
{1, 8, 22, 92},
{1, 12, 34, 188, 716},
{1, 14, 40, 248, 976, 4928},
{1, 18, 52, 392, 1616, 9504, 44864},
{1, 20, 58, 476, 1996, 12560, 61048, 348176},
{1, 24, 70, 668, 2876, 20448, 104168, 658192, 3608080},
{1, 30, 88, 1016, 4496, 37440, 200768, 1449856, 8521216, 57638400}

Mathematica

Binet[n_, m_] = ((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2; a = Table[Table[ExpandAll[Binet[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[a]

Crossrefs

Sequence in context: A298829 A056140 A225419 * A343599 A191714 A370356

Adjacent sequences: A140892 A140893 A140894 * A140896 A140897 A140898

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Jul 23 2008

Extensions

Edited by N. J. A. Sloane, Aug 01 2008

Status

approved