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A087445
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Numbers that are congruent to {1, 5} mod 12.
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2
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1, 5, 13, 17, 25, 29, 37, 41, 49, 53, 61, 65, 73, 77, 85, 89, 97, 101, 109, 113, 121, 125, 133, 137, 145, 149, 157, 161, 169, 173, 181, 185, 193, 197, 205, 209, 217, 221, 229, 233, 241, 245, 253, 257, 265, 269, 277, 281, 289, 293, 301, 305, 313, 317, 325, 329
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
| G.f.: x*(1+4*x+7*x^2)/((1+x)*(1-x)^2); E.g.f.: 6xexp(x)+exp(-x); a(n)=6n+(-1)^n.
a(n)=6*(n-1)-(-1)^n [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Aug 04 2009]
a(n)=12*n-a(n-1)-18 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
a(0)=1, a(1)=5, a(2)=13, a(n)=a(n-1)+a(n-2)-a(n-3) [From Harvey P. Dale, June 13 2011]
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EXAMPLE
| For n=2, a(2)=12*2-1-18=5; n=3, a(3)=12*3-5-18=13; n=4, a(4)=12*4-13-18=17 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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MATHEMATICA
| LinearRecurrence[{1, 1, -1}, {1, 5, 13}, 70] (* or *) Rest[CoefficientList[ Series[x (1+4x+7x^2)/((1+x)(1-x)^2), {x, 0, 70}], x]] (* From Harvey P. Dale, June 13 2011 *)
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CROSSREFS
| Cf. A001651, A047241, A087444, A087446.
Sequence in context: A105596 A037046 A126887 * A020882 A081804 A004613
Adjacent sequences: A087442 A087443 A087444 * A087446 A087447 A087448
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 04 2003
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