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A016208
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Expansion of 1/((1-x)(1-3x)(1-4x)).
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6
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..24.
Index to sequences with linear recurrences with constant coefficients, signature (8,-19,12)
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FORMULA
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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) [From Harvey P. Dale, Apr 09 2012]
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MAPLE
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a:=n->sum(4^(n-j)-3^(n-j), j=0..n): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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MATHEMATICA
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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}](*From 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] (* From Harvey P. Dale, Apr 09 2012 *)
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PROG
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(PARI) Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
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CROSSREFS
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Cf. A000225, A000295, A000392, A002275, A003462, A003463, A003464, A023000, A023001, A002452, A016123, A016125, A016256.
Sequence in context: A055222 A026015 A002696 * A216540 A026852 A110609
Adjacent sequences: A016205 A016206 A016207 * A016209 A016210 A016211
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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