VOOZH about

URL: https://oeis.org/A077937

⇱ A077937 - OEIS

login
A077937
Expansion of 1/(1-2*x-2*x^2+2*x^3).
12
1, 2, 6, 14, 36, 88, 220, 544, 1352, 3352, 8320, 20640, 51216, 127072, 315296, 782304, 1941056, 4816128, 11949760, 29649664, 73566592, 182532992, 452899840, 1123732480, 2788198656, 6918062592, 17165057536, 42589842944, 105673675776, 262196922368
OFFSET
0,2
COMMENTS
Form the graph with matrix A = [1,1,1,1; 1,0,0,0; 1,0,0,0; 1,0,0,1]. Then the sequence 0, 1, 2, 6, ... counts walks of length n between the degree 5 vertex and the degree 3 vertex. - Paul Barry, Oct 02 2004
From Sean A. Irvine, Jun 05 2025: (Start)
Also, the number of walks of length n starting at vertex 0 in the graph:
1-2
/| |
0 | |
\| |
4-3. (End)
FORMULA
a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0) = 1, a(1) = 2, and a(3) = 8. - G. C. Greubel, May 02 2022
MATHEMATICA
LinearRecurrence[{2, 2, -2}, {1, 2, 6}, 50] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)
CoefficientList[Series[1/(1-2*x-2*x^2+2*x^3), {x, 0, 40}], x] (* Harvey P. Dale, Dec 05 2018 *)
PROG
(PARI) Vec(1/(1-2*x-2*x^2+2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
(Magma) [n le 3 select Factorial(n) else 2*(Self(n-1) +Self(n-2) -Self(n-3)): n in [1..51]]; // G. C. Greubel, May 02 2022
(SageMath)
def A077937_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-2*x^2+2*x^3) ).list()
A077937_list(50) # G. C. Greubel, May 02 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved