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A086901 a(1) = a(2) = 1; for n>2, a(n) = 4*a(n-1) + 3*a(n-2). 6
1, 1, 7, 31, 145, 673, 3127, 14527, 67489, 313537, 1456615, 6767071, 31438129, 146053729, 678529303, 3152278399, 14644701505, 68035641217, 316076669383, 1468413601183, 6821884412881, 31692778455073, 147236767058935 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = ((c + 5)b^n - (b + 5)c^n)/14, where b = 2 + sqrt(7), c = 2 - sqrt(7).

From Ralf Stephan, Feb 01 2004: (Start)

G.f.: x(1-3x)/(1 - 4x - 3x^2).

a(n) = A015530(n) - 3*A015530(n-1) = 1 + 6*sum_{k=0..n} A015530(k)). (End)

a(n+1) = sum_{k=0..n} 3^(n-k)*A122542(n,k), n>=0. - Philippe Deléham, Oct 27 2006

a(n) = upper left term in the 2 X 2 matrix [1,2; 3,3]^(n-1). - Gary W. Adamson, Mar 02 2008

a(n) = (1/14)*(2-sqrt(7))^n*sqrt(7) - (1/14)*sqrt(7)*(2+sqrt(7))^n + (1/2)*(2-sqrt(7))^n + (1/2)*(2+sqrt(7))^n, with n>=0. - Paolo P. Lava, Nov 20 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

EXAMPLE

a(3) = 4*1 + 3*1 = 7;

a(4) = 4*7 + 3*1 = 31.

MATHEMATICA

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 *)

PROG

(PARI) A086901(n)=if(n<3, 1, 4*A086901(n-1)+3*A086901(n-2)) \\ Michael B. Porter, Apr 04 2010

(Haskell)

a086901 n = a086901_list !! (n-1)

a086901_list = 1 : 1 : zipWith (+)

               (map (* 3) a086901_list) (map (* 4) $ tail a086901_list)

-- Reinhard Zumkeller, Feb 13 2015

CROSSREFS

Cf. A102900.

Sequence in context: A044049 A255284 A005825 * A003526 A121517 A199216

Adjacent sequences:  A086898 A086899 A086900 * A086902 A086903 A086904

KEYWORD

easy,nonn

AUTHOR

Rick Powers (rick.powers(AT)mnsu.edu), Sep 18 2003

EXTENSIONS

More terms from Ray Chandler, Sep 19 2003

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)