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A275932 a(n) = F(2*n+6)*F(2*n+2)^3, where F = Fibonacci (A000045). 1

%I #20 Sep 08 2022 08:46:17

%S 8,567,28160,1333584,62723375,2947166208,138457523672,6504579992295,

%T 305576963500544,14355613810692000,674408279720748383,

%U 31682833585030397952,1488418770572887642280,69923999385781980681879,3284939552377913067968000,154322234962490820966855408

%N a(n) = F(2*n+6)*F(2*n+2)^3, where F = Fibonacci (A000045).

%C The right-hand side of Helmut Postl's identity F(2n+6) + F(n)*F(n+4)^3 = F(n+6)*F(n+2)^3, n even.

%H Colin Barker, <a href="/A275932/b275932.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (55,-385,385,-55,1).

%F From _Colin Barker_, Aug 31 2016: (Start)

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

%F G.f.: (8+127*x+55*x^2-x^3) / ((1-x)*(1-47*x+x^2)*(1-7*x+x^2)).

%F (End)

%t Table[(Fibonacci[2 n + 6] Fibonacci[2 n + 2]^3), {n, 0, 20}] (* _Vincenzo Librandi_, Sep 02 2016 *)

%o (PARI) Vec((8+127*x+55*x^2-x^3)/((1-x)*(1-47*x+x^2)*(1-7*x+x^2)) + O(x^20)) \\ _Colin Barker_, Aug 31 2016

%o (Magma) [Fibonacci(2*n+6)*Fibonacci(2*n+2)^3: n in [0..25]]; // _Vincenzo Librandi_, Sep 02 2016

%Y Cf. A000045.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Aug 31 2016

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Last modified July 25 00:10 EDT 2024. Contains 374585 sequences. (Running on oeis4.)