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A097813
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a(n) = 3*2^n - 2*n - 2.
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6
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1, 2, 6, 16, 38, 84, 178, 368, 750, 1516, 3050, 6120, 12262, 24548, 49122, 98272, 196574, 393180, 786394, 1572824, 3145686, 6291412, 12582866, 25165776, 50331598, 100663244, 201326538, 402653128, 805306310, 1610612676, 3221225410, 6442450880, 12884901822, 25769803708
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OFFSET
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0,2
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COMMENTS
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An elephant sequence, see A175654. For the corner squares four A[5] vectors, with decimal values 58, 154, 178 and 184, lead to this sequence. For the central square these vectors lead to the companion sequence A033484. - Johannes W. Meijer, Aug 15 2010
a(n) is also the number of order-preserving partial isometries of an n-chain, i.e., the row sums of A183153 and A183154. - Abdullahi Umar, Dec 28 2010
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LINKS
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FORMULA
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G.f.: (1 - 2*x + 3*x^2)/((1-x)^2*(1-2*x)).
a(n) = 2*a(n-1) + 2*n - 2, for n>0, with a(0)=1.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
E.g.f.: 3*exp(2*x) - 2*(1 + x)*exp(x). (End)
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MATHEMATICA
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Table[3 2^n-2n-2, {n, 0, 40}] (* or *) LinearRecurrence[{4, -5, 2}, {1, 2, 6}, 40] (* Harvey P. Dale, Oct 25 2011 *)
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PROG
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(Magma) [3*2^n -2*(n+1): n in [0..40]]; // G. C. Greubel, Dec 30 2021
(Sage) [3*2^n -2*(n+1) for n in (0..40)] # G. C. Greubel, Dec 30 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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