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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 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..35.

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: A094084 A042829 A232110 * A005326 A298561 A226049

Adjacent sequences:  A140893 A140894 A140895 * A140897 A140898 A140899

KEYWORD

nonn,uned,tabl

AUTHOR

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

STATUS

approved

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Last modified October 23 21:27 EDT 2021. Contains 348217 sequences. (Running on oeis4.)