A140894 Triangle T(n,k) = sum_{0<=j<=k/2} A034867(k,j)*prime(n)^j, read by rows, 0<=k<n.

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

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