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A084170
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5*2^n/3 + (-1)^n/3 - 1.
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4
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1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, 3412, 6826, 13652, 27306, 54612, 109226, 218452, 436906, 873812, 1747626, 3495252, 6990506, 13981012, 27962026, 55924052, 111848106, 223696212, 447392426, 894784852, 1789569706, 3579139412
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Original name of this sequence: Generalized Jacobsthal numbers.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2).
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FORMULA
| a(n) = 2*a(n-1) +a(n-2) -2*a(n-3), n>2.
a(n)=a(n-1)+2*a(n-2)+2, a(0)=1, a(1)=2.
G.f.:(1+x^2)/((1+x)*(1-x)*(1-2*x)).
E.g.f.: 5*exp(2*x)/3-exp(x)+exp(-x)/3.
a(n+1) = A000975(n+2)+A000975(n).
a(2*n+1)-2 = 10*A000975(n); a(2*n+2)-6 = 20*A000975(n).
a(n+2*k) -a(n) = 5*A002450(k)*2^n = A146882(k-1)*2^n, k=0,1,2,... - Paul Curtz, Jun 15 2011
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MATHEMATICA
| LinearRecurrence[{2, 1, -2}, {1, 2, 6}, 40] (* or *) Table[5*2^n/3+(-1)^n/3-1, {n, 0, 40}] (* From Harvey P. Dale, Jan 29 2012 *)
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PROG
| (PARI) a(n)=(5*2^n)\/3-1 \\ Charles R Greathouse IV, Jul 01 2011
(MAGMA) [5*2^n/3 + (-1)^n/3 - 1: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
| Sequence in context: A136515 A141347 A054454 * A052971 A029863 A091919
Adjacent sequences: A084167 A084168 A084169 * A084171 A084172 A084173
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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