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A016208 Expansion of 1/((1-x)*(1-3*x)*(1-4*x)). 8
1, 8, 45, 220, 1001, 4368, 18565, 77540, 320001, 1309528, 5326685, 21572460, 87087001, 350739488, 1410132405, 5662052980, 22712782001, 91044838248, 364760483725, 1460785327100, 5848371485001, 23409176469808, 93683777468645, 374876324642820, 1499928942876001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A085277. - Paul Barry, Jun 25 2003

Number of walks of length 2n+5 between two nodes at distance 5 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (8,-19,12)

FORMULA

a(n) = 16*4^n/3+1/6-9*3^n/2. - Paul Barry, Jun 25 2003

a(0) = 0, a(1) = 8, a(n) = 7*a(n-1)-12*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(0) = 1, a(1) = 8, a(2) = 45, a(n) = 8*a(n-1)-19*a(n-2)+12*a(n-3). - Harvey P. Dale, Apr 09 2012

MAPLE

a:= n-> add(4^(n-j+1)-3^(n-j+1), j=0..n+1): seq(a(n), n=0..24); # - Zerinvary Lajos, Jan 04 2007

MATHEMATICA

Join[{a=1, b=8}, Table[c=7*b-12*a+1; a=b; b=c, {n, 60}]] (* and *) Table[(2^(2*n + 3) - 3^(n + 2) + 1)/6, {n, 40}](* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *)

CoefficientList[Series[1/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {8, -19, 12}, {1, 8, 45}, 30] (* Harvey P. Dale, Apr 09 2012 *)

PROG

(PARI) Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A000225, A000295, A000392, A002275, A003462, A003463, A003464, A023000, A023001, A002452, A016123, A016125, A016256.

Sequence in context: A273305 A026015 A002696 * A216540 A026852 A110609

Adjacent sequences:  A016205 A016206 A016207 * A016209 A016210 A016211

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 3 17:01 EST 2016. Contains 278745 sequences.