A138199 a(n) = 14^(2*n+1) + 3^(2*n+1).

17, 2771, 538067, 105415691, 20661066467, 4049565346811, 793714774848467, 155568095572161131, 30491346729460336067, 5976303958950076658651, 1171355575953997682201267, 229585692886981589625399371, 44998795805848373961803836067, 8819763977946281138070581903291

Offset: 0

Author

Reinhard Zumkeller, Mar 05 2008

Keywords

• nonn
• easy

Comments

Subsequence of A008599; A138200(n) = a(n)/17.

References

• F. Ischebeck, Einladung zur Zahlentheorie (BI Wissenschaftsverlag 1992), Aufgabe 7, p. 18.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (205, -1764).

Crossrefs

Cf. A008599, A076311, A138200.

Programs

Magma

[14^(2*n+1)+3^(2*n+1): n in [0..20]]; // Vincenzo Librandi, Dec 27 2010

Mathematica

Table[c=2n+1;14^c+3^c,{n,0,20}] (* or *) LinearRecurrence[{205,-1764},{17,2771},30] (* Harvey P. Dale, Aug 13 2013 *)
CoefficientList[Series[14/(1 - 196 x) + 3/(1 - 9 x), {x, 0, 25}], x] (* Vincenzo Librandi, May 23 2014 *)

Formula

a(0)=17, a(1)=2771; a(n) = 205*a(n-1)-1764*a(n-2). - Harvey P. Dale, Aug 13 2013

G.f.: 14/(1-196*x)+3/(1-9*x). -Harvey P. Dale, Aug 13 2013

Extensions

Corrected and extended by Harvey P. Dale, Aug 13 2013