A136201 a(n) = 2*a(n-1) + 4*a(n-2) - 6*a(n-3) - 3*a(n-4).
0, 0, 0, 1, 2, 8, 18, 53, 124, 328, 780, 1969, 4718, 11648, 28014, 68405, 164824, 400240, 965304, 2337409, 5640122, 13637336, 32914794, 79525973, 191966740, 463636600, 1119239940, 2702647921, 6524535782, 15753313808, 38031163398
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,4,-6,-3).
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
-
Maple
a:=proc(n) options operator, arrow: expand((1/8)*(1+sqrt(2))^n+(1/8)*(1-sqrt(2))^n+(1/24)*3^((1/2)*n)*(-3-sqrt(3)-3*(-1)^n+(-1)^n*sqrt(3))) end proc: seq(a(n),n=0..30); # Emeric Deutsch, Mar 31 2008
-
Mathematica
LinearRecurrence[{2, 4, -6, -3}, {0, 0, 0, 1}, 50] (* G. C. Greubel, Feb 23 2017 *) CoefficientList[Series[x^3/(1-2 x-4 x^2+6 x^3+3 x^4),{x,0,50}],x] (* Harvey P. Dale, Apr 21 2022 *) -
PARI
x='x+O('x^50); Vec(x^3/(3*x^4 + 6*x^3 - 4*x^2 - 2*x + 1)) \\ G. C. Greubel, Feb 23 2017
Formula
a(n) = (1/8)*(1+sqrt(2))^n + (1/8)*(1-sqrt(2))^n + (1/24)*3^(n/2)*(-3 - sqrt(3) - 3(-1)^n + (-1)^n*sqrt(3)). - Emeric Deutsch, Mar 31 2008
G.f.: x^3/(3*x^4 + 6*x^3 - 4*x^2 - 2*x + 1). - Alexander R. Povolotsky, Mar 31 2008
Comments