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A102901
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a(n) = a(n-1) + 6a(n-2), a(0)=1, a(1)=0.
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6
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1, 0, 6, 6, 42, 78, 330, 798, 2778, 7566, 24234, 69630, 215034, 632814, 1923018, 5719902, 17258010, 51577422, 155125482, 464590014, 1395342906, 4182882990, 12554940426, 37652238366, 112981880922, 338895311118, 1016786596650
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OFFSET
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0,3
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COMMENTS
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Binomial transform is A102900.
Hankel transform is := 1,6,0,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008
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REFERENCES
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Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,6).
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FORMULA
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G.f.: (1-x)/((1+2*x)*(1-3*x))
a(n) = (2*3^n+3*(-2)^n)/5.
a(n) = 6*A015441(n-1), for n>0.
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EXAMPLE
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a(6) = 330; (2*3^6 + 3*(-2)^6)/5 = (1458 + 192)/5 = 330.
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MAPLE
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A102901:=n->(2*3^n+3*(-2)^n)/5; seq(A102901(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013
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MATHEMATICA
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CoefficientList[Series[(1 - x) / ((1 + 2 x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 20 2013 *)
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PROG
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(MAGMA) [(2*3^n+3*(-2)^n)/5: n in [0..30]]; // Vincenzo Librandi, Jul 20 2013
(PARI) a(n)=([0, 1; 6, 1]^n*[1; 0])[1, 1] \\ Charles R Greathouse IV, Mar 28 2016
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CROSSREFS
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Cf. A015441.
Sequence in context: A125510 A117859 A229159 * A014435 A175550 A219352
Adjacent sequences: A102898 A102899 A102900 * A102902 A102903 A102904
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jan 17 2005
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STATUS
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approved
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