A124152 a(n) = Fibonacci(6, n).
0, 8, 70, 360, 1292, 3640, 8658, 18200, 34840, 61992, 104030, 166408, 255780, 380120, 548842, 772920, 1065008, 1439560, 1912950, 2503592, 3232060, 4121208, 5196290, 6485080, 8017992, 9828200, 11951758, 14427720, 17298260, 20608792, 24408090, 28748408
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
-
Maple
with(combinat, fibonacci):seq(fibonacci(6, i), i=0..35);
-
Mathematica
LinearRecurrence[{6,-15,20,-15,6,-1},{0,8,70,360,1292,3640},40] (* Harvey P. Dale, Apr 18 2019 *) -
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
-
Sage
[lucas_number1(6,n,-1) for n in range(0, 30)] # Zerinvary Lajos, May 16 2009
Formula
From Colin Barker, Apr 06 2017: (Start)
G.f.: 2*x*(4 + 11*x + 30*x^2 + 11*x^3 + 4*x^4) / (1 - x)^6.
a(n) = n*(3 + 4*n^2 + n^4).
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.
(End)