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A140894 Triangle T(n,k) = sum_{0<=j<=k/2} A034867(k,j)*prime(n)^j, read by rows, 0<=k<n. 0
1, 1, 2, 1, 2, 8, 1, 2, 10, 32, 1, 2, 14, 48, 236, 1, 2, 16, 56, 304, 1280, 1, 2, 20, 72, 464, 2080, 11584, 1, 2, 22, 80, 556, 2552, 15112, 76160, 1, 2, 26, 96, 764, 3640, 24088, 128256, 786448, 1, 2, 32, 120, 1136, 5632, 43072, 243840, 1693696, 10214912 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are 1, 3, 11, 45, 301, 1659, 14223, 94485, 943321, 12202443...

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,m)=( (1+sqrt prime(n))^m - (1-sqrt prime(n))^m) / (2*sqrt prime(n)).

EXAMPLE

1;

1, 2;

1, 2, 8;

1, 2, 10, 32;

1, 2, 14, 48, 236;

1, 2, 16, 56, 304, 1280;

1, 2, 20, 72, 464, 2080, 11584;

1, 2, 22, 80, 556, 2552, 15112, 76160;

1, 2, 26, 96, 764, 3640, 24088, 128256, 786448;

1, 2, 32, 120, 1136, 5632, 43072, 243840, 1693696, 10214912;

MATHEMATICA

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

CROSSREFS

Cf. A117809.

Sequence in context: A179946 A198757 A173755 * A208747 A334729 A221878

Adjacent sequences:  A140891 A140892 A140893 * A140895 A140896 A140897

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)