OFFSET
1,1
COMMENTS
Row sums are:
{3, 32, 638, 16916, 1189512, 47845830, 4464390458, 239790743824, 28080250874340, 6507897094710230}.
The idea of multiplying the Lucas type Binet by the Fibonacci type Binet gave this result.
LINKS
Arthur T. Benjamin, Jennifer J. Quinn, Fibonacci and Lucas Identities through Colored Tilings, Utilitas Mathematica, Vol 56, pp. 137-142, November, 1999.
FORMULA
t(n,m)=((( 1 + sqrt(prime(n))))^(2*m) + (( 1 - sqrt(prime(n))))^(2*m))/2.
EXAMPLE
{3},
{4, 28},
{6, 56, 576},
{8, 92, 1184, 15632},
{12, 188, 3312, 60688, 1125312},
{14, 248, 4928, 102272, 2153984, 45584384},
{18, 392, 9504, 241792, 6271488, 163874816, 4293992448},
{20, 476, 12560, 348176, 9857600, 281494976, 8065936640, 231433093376},
{24, 668, 20448, 658192, 21696384, 722861504, 24196302336, 811557544192, 27243751790592},
{30, 1016, 37440, 1449856, 57638400, 2321616896, 94108508160, 3826362843136, 155800700190720, 6348173542424576}
MATHEMATICA
Binet[n_, m_] = ((( 1 + Sqrt[Prime[n]]))^(2m) + (( 1 - Sqrt[Prime[n]]))^(2*m))/(2); a = Table[Table[ExpandAll[Binet[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[a]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula and Gary W. Adamson, Jul 23 2008
STATUS
approved