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A094723
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a(n) = Pell(n+2) - 2^n.
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3
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1, 3, 8, 21, 54, 137, 344, 857, 2122, 5229, 12836, 31413, 76686, 186833, 454448, 1103921, 2678674, 6494037, 15732284, 38089677, 92173782, 222961529, 539145416, 1303349513, 3150038746, 7611815613, 18390447188, 44426264421, 107310084894
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OFFSET
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0,2
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COMMENTS
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The sequence b(n) = 2*a(n), n >= -1, is an elephant sequence, see A175654. For the corner squares 24 A[5] vectors, with decimal values between 23 and 464, lead to the b(n) sequence. For the central square these vectors lead to the companion sequence A175658. - Johannes W. Meijer, Aug 15 2010
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LINKS
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FORMULA
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G.f.: (1 - x - x^2)/((1-2*x)*(1 - 2*x - x^2)).
a(n) = ((1+sqrt(2))^n*(3*sqrt(2)/4+1) - (3*sqrt(2)/4-1)*(1-sqrt(2))^n) - 2^n.
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MATHEMATICA
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PROG
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(Magma) I:=[1, 3, 8]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 24 2012
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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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