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A086901
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a(1) = a(2) = 1; for n>2, a(n) = 4*a(n-1) + 3*a(n-2).
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6
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1, 1, 7, 31, 145, 673, 3127, 14527, 67489, 313537, 1456615, 6767071, 31438129, 146053729, 678529303, 3152278399, 14644701505, 68035641217, 316076669383, 1468413601183, 6821884412881, 31692778455073, 147236767058935
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = ((c + 5)*b^n - (b + 5)*c^n)/14, where b = 2 + sqrt(7), c = 2 - sqrt(7).
G.f.: x(1-3x)/(1 - 4x - 3x^2).
a(n) = upper left term in the 2 X 2 matrix [1,2; 3,3]^(n-1). - Gary W. Adamson, Mar 02 2008
G.f.: G(0)*(1-3*x)/(2-4*x), where G(k) = 1 + 1/(1 - x*(7*k-4)/(x*(7*k+3) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 16 2013
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EXAMPLE
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a(3) = 4*1 + 3*1 = 7;
a(4) = 4*7 + 3*1 = 31.
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MATHEMATICA
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a[n_]:=(MatrixPower[{{3, 2}, {3, 1}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{3, 4}, #]}]&, {1, 1}, 40]][[1]] (* Harvey P. Dale, Mar 23 2011 *)
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PROG
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(Haskell)
a086901 n = a086901_list !! (n-1)
a086901_list = 1 : 1 : zipWith (+)
(map (* 3) a086901_list) (map (* 4) $ tail a086901_list)
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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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Rick Powers (rick.powers(AT)mnsu.edu), Sep 18 2003
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EXTENSIONS
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STATUS
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approved
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