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A140896
An even-powered type Binet p-adic triangular sequence: t(n,m)=((( 1 + sqrt(prime(n))))^(2*m) + (( 1 - sqrt(prime(n))))^(2*m))/2.
0
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
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
Sequence in context: A367388 A042829 A232110 * A005326 A298561 A226049
KEYWORD
nonn,uned,tabl
AUTHOR
STATUS
approved