A007829 From random walks on complete directed triangle.

0, 0, 0, 0, 0, 6, 8, 28, 44, 100, 162, 318, 514, 942, 1518, 2672, 4302, 7380, 11882, 20040, 32276, 53810, 86710, 143396, 231204, 380152, 613286, 1004188, 1620864, 2645928, 4272744, 6959326, 11242518, 18281222, 29542078, 47978666, 77552928, 125836374, 203445784

Offset

0,6

Links

Sean A. Irvine, Table of n, a(n) for n = 0..500

E. Bussian, Email to N. J. A. Sloane, Oct. 1994

Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-4,5,5,-2,-2).

Formula

From Colin Barker, Feb 03 2018: (Start)

G.f.: 2*x^5*(3 - 2*x - 3*x^2) / ((1 - x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x^2 - x^3)).

a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3) - 4*a(n-4) + 5*a(n-5) + 5*a(n-6) - 2*a(n-7) - 2*a(n-8) for n>7.

(End)

From G. C. Greubel, Mar 11 2020: (Start)

a(n) = 2*(2 + Fibonacci(n+2) - 2^floor(n/2) - A084338(n+2)).

a(n) = 2*(2 + Fibonacci(n+2) - 2^floor(n/2) - b(n+7) - b(n+5)), where b(n) = A000931(n). (End)

Maple

m:=35; S:=series(2*x^5*(3-2*x-3*x^2)/((1-x)*(1-x-x^2)*(1-2*x^2)*(1-x^2-x^3)), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Mar 11 2020

Mathematica

b[n_]:= b[n]= If[n==0, 1, If[n<3, 0, b[n-2] +b[n-3]]]; Table[2*(2 +Fibonacci[n+2] -2^Floor[n/2] -p[n+7] -p[n+5]), {n, 0, 35}] (* G. C. Greubel, Mar 11 2020 *)

Prog

(Sage)
def A007829_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 2*x^5*(3-2*x-3*x^2)/((1-x)*(1-x-x^2)*(1-2*x^2)*(1-x^2-x^3)) ).list()
A007829_list(35) # G. C. Greubel, Mar 11 2020

Crossrefs

Cf. A000931, A084338.

Sequence in context: A267477 A237290 A229335 * A345003 A000773 A258283

Adjacent sequences: A007826 A007827 A007828 * A007830 A007831 A007832

Keyword

nonn,walk

Author

Eric Bussian [ ebussian(AT)math.gatech.edu ]

Status

approved