login
a(n) = Fibonacci(6, n).
5

%I #11 Dec 07 2019 12:18:25

%S 0,8,70,360,1292,3640,8658,18200,34840,61992,104030,166408,255780,

%T 380120,548842,772920,1065008,1439560,1912950,2503592,3232060,4121208,

%U 5196290,6485080,8017992,9828200,11951758,14427720,17298260,20608792,24408090,28748408

%N a(n) = Fibonacci(6, n).

%H Colin Barker, <a href="/A124152/b124152.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F From _Colin Barker_, Apr 06 2017: (Start)

%F G.f.: 2*x*(4 + 11*x + 30*x^2 + 11*x^3 + 4*x^4) / (1 - x)^6.

%F a(n) = n*(3 + 4*n^2 + n^4).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

%F (End)

%p with(combinat, fibonacci):seq(fibonacci(6, i), i=0..35);

%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,8,70,360,1292,3640},40] (* _Harvey P. Dale_, Apr 18 2019 *)

%o (Sage) [lucas_number1(6,n,-1) for n in range(0, 30)] # _Zerinvary Lajos_, May 16 2009

%o (PARI) concat(0, Vec(2*x*(4 + 11*x + 30*x^2 + 11*x^3 + 4*x^4) / (1 - x)^6 + O(x^30))) \\ _Colin Barker_, Apr 06 2017

%Y Cf. A117715 formatted as a triangular array: row 7.

%Y Cf. A000045.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Dec 01 2006