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1, 7, 17, 55, 161, 487, 1457, 4375, 13121, 39367, 118097, 354295, 1062881, 3188647, 9565937, 28697815, 86093441, 258280327, 774840977, 2324522935, 6973568801, 20920706407, 62762119217, 188286357655, 564859072961, 1694577218887
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A081631. Inverse binomial transform of A081654.
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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 (2,3).
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FORMULA
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G.f.: (1+5*x)/((1-3*x)(1+x)).
E.g.f. 2*exp(3*x)-exp(-x).
a(0)=1, a(1)=7, a(n)=2*a(n-1)+3*a(n-2) [ Harvey P. Dale, May 24 2011]
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MATHEMATICA
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Total/@Partition[Riffle[2*3^Range[0, 30], {-1, 1}], 2] (* or *) LinearRecurrence[{2, 3}, {1, 7}, 30] (* Harvey P. Dale, May 24 2011 *)
CoefficientList[Series[(1 + 5 x) / ((1 - 3 x) (1 + x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
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PROG
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(Magma) [2*3^n-(-1)^n: n in [0..40]]; // Vincenzo Librandi, Aug 10 2013
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CROSSREFS
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Sequence in context: A352616 A094534 A262106 * A276907 A293464 A106010
Adjacent sequences: A081629 A081630 A081631 * A081633 A081634 A081635
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Mar 26 2003
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STATUS
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approved
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