A356760 a(n) = L(2*F(n)) + L(2*F(n+1)), where L(n) is the n-th Lucas number (A000032), and F(n) is the n-th Fibonacci number (A000045).

5, 6, 10, 25, 141, 2330, 273650, 599346021, 162615199748425, 97418273437938007563970, 15841633607002514292104722681296528726, 1543264591854508694059707631430587191184612139118583889182925

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..16

Hideyuki Ohtsuka, Problem H-901, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 60, No. 3 (2022), p. 281.

Formula

a(n) = A000032(2*A000045(n)) + A000032(2*A000045(n+1)).

a(n) = A316275(n) + A316275(n+1).

Sum_{n>=0} (-1)^n/a(n) = 1/10 (Ohtsuka, 2022).

Mathematica

a[n_] := LucasL[2*Fibonacci[n]] + LucasL[2*Fibonacci[n + 1]]; Array[a, 12, 0]

Crossrefs

Cf. A000032, A000045, A316275, A356761.

Sequence in context: A075904 A018834 A029943 * A063630 A342127 A119102

Adjacent sequences: A356757 A356758 A356759 * A356761 A356762 A356763

Keyword

nonn

Author

Amiram Eldar, Aug 26 2022

Status

approved