A049656 a(n) = (F(8n+7)-1)/3, where F=A000045 (the Fibonacci sequence).

4, 203, 9552, 448756, 21081995, 990405024, 46527954148, 2185823439947, 102687173723376, 4824111341558740, 226630545879537419, 10646811544996699968, 500173512068965361092, 23497508255696375271371, 1103882714505660672393360, 51858990073510355227216564

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (48,-48,1).

Formula

G.f.: ( -4-11*x ) / ( (x-1)*(x^2-47*x+1) ). - R. J. Mathar, Oct 26 2015

a(n) = (-1+((94+42*sqrt(5))^(-n)*(4^n*(1+sqrt(5))+2*(47+21*sqrt(5))^(2*n)*(682+305*sqrt(5))))/(105+47*sqrt(5)))/3. - Colin Barker, Mar 06 2016

a(n) = 47*a(n-1)-a(n-2)+15. - Vincenzo Librandi, Mar 06 2016

Mathematica

(Fibonacci[8Range[0, 20]+7]-1)/3 (* Harvey P. Dale, Sep 21 2011 *)
RecurrenceTable[{a[0] == 4, a[1] == 203, a[n] == 47 a[n-1] - a[n-2] + 15}, a, {n, 30}] (* Vincenzo Librandi, Mar 06 2016 *)

Prog

(PARI) Vec((-4-11*x)/((x-1)*(x^2-47*x+1)) + O(x^25)) \\ Colin Barker, Mar 06 2016
(Magma) I:=[4, 203]; [n le 2 select I[n] else 47*Self(n-1)-Self(n-2)+15: n in [1..30]]; // Vincenzo Librandi, Mar 06 2016

Crossrefs

Cf. A049655, A049686.

Sequence in context: A174776 A216932 A317273 * A129465 A300152 A260639

Adjacent sequences: A049653 A049654 A049655 * A049657 A049658 A049659

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved