A275931 a(n) = F(2*n+3)*F(2*n+1)^3, where F = Fibonacci (A000045).

2, 40, 1625, 74698, 3498056, 164257777, 7716095570, 362488657000, 17029226266313, 800010977816986, 37583485579350152, 1765623803357209825, 82946735218100281250, 3896730931076485826728, 183063407022834751530041, 8600083399124733831953002, 404020856351720236303380680

Offset

0,1

Comments

The right-hand side of Helmut Postl's identity F(2n+3) + F(n)*F(n+2)^3 = F(n+3)*F(n+1)^3, n even.

Links

Colin Barker, Table of n, a(n) for n = 0..550

Index entries for linear recurrences with constant coefficients, signature (55,-385,385,-55,1).

Formula

From Colin Barker, Aug 31 2016: (Start)

a(n) = 55*a(n-1)-385*a(n-2)+385*a(n-3)-55*a(n-4)+a(n-5) for n>4.

G.f.: (2-70*x+195*x^2-47*x^3+x^4) / ((1-x)*(1-47*x+x^2)*(1-7*x+x^2)).

(End)

Mathematica

Table[(Fibonacci[2 n + 3] Fibonacci[2 n + 1]^3), {n, 0, 20}] (* Vincenzo Librandi, Sep 02 2016 *)
LinearRecurrence[{55, -385, 385, -55, 1}, {2, 40, 1625, 74698, 3498056}, 20] (* Harvey P. Dale, Aug 09 2019 *)

Prog

(PARI) Vec((2-70*x+195*x^2-47*x^3+x^4)/((1-x)*(1-47*x+x^2)*(1-7*x+x^2)) + O(x^20)) \\ Colin Barker, Aug 31 2016
(Magma) [Fibonacci(2*n+3)*Fibonacci(2*n+1)^3: n in [0..25]]; // Vincenzo Librandi, Sep 02 2016

Crossrefs

Cf. A000045.

Sequence in context: A012241 A341589 A286124 * A099707 A198248 A261732

Adjacent sequences: A275928 A275929 A275930 * A275932 A275933 A275934

Keyword

nonn

Author

N. J. A. Sloane, Aug 31 2016

Status

approved