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A123752
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a(n) = 7*a(n-2), a(0) = 1, a(1) = 2.
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1
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1, 2, 7, 14, 49, 98, 343, 686, 2401, 4802, 16807, 33614, 117649, 235298, 823543, 1647086, 5764801, 11529602, 40353607, 80707214, 282475249, 564950498, 1977326743, 3954653486, 13841287201, 27682574402, 96889010407, 193778020814
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OFFSET
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0,2
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COMMENTS
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The first 2n terms are the divisors of 2 * 7^(n - 1). - Alonso del Arte, Jul 14 2016
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,7).
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FORMULA
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a(n) = 7^(n/2)*(7*(1+(-1)^n) + 2*sqrt(7)*(1-(-1)^n))/14.
From R. J. Mathar, Jun 18 2008: (Start)
O.g.f.: (1 + 2*x)/(1 - 7*x^2).
a(2n) = A000420(n). a(2n+1) = 2*A000420(n). (End)
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
E.g.f.: cosh(sqrt(7)*x) + 2*sinh(sqrt(7)*x)/sqrt(7). - G. C. Greubel, Aug 10 2019
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MAPLE
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a[0]:=1: a[1]:=2: for n from 2 to 30 do a[n]:=7*a[n-2] od: seq(a[n], n=0..30);
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MATHEMATICA
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LinearRecurrence[{0, 7}, {1, 2}, 30] (* Harvey P. Dale, Mar 21 2013 *)
halfMax = 13; Divisors[2 * 7^halfMax] (* Alonso del Arte, Jul 18 2016 *)
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PROG
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(MAGMA) [n le 2 select n else 7*Self(n-2): n in [1..30]]; //Vincenzo Librandi, Jul 25 2016
(PARI) a(n)=if(n%2, 2, 1)*7^(n\2) \\ Charles R Greathouse IV, Jul 25 2016
(Sage) [7^(n/2)*(7*(1+(-1)^n) + 2*sqrt(7)*(1-(-1)^n))/14 for n in (0..30)] # G. C. Greubel, Aug 10 2019
(GAP) a:=[1, 2];; for n in [3..30] do a[n]:=7*a[n-2]; od; a; # G. C. Greubel, Aug 10 2019
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CROSSREFS
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Cf. A018592.
Sequence in context: A128882 A018281 A018592 * A192507 A018622 A018668
Adjacent sequences: A123749 A123750 A123751 * A123753 A123754 A123755
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KEYWORD
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nonn,easy
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, Nov 15 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Nov 29 2006
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STATUS
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approved
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