A156161 a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=289, a(2)=7225.
289, 7225, 243049, 8254129, 280395025, 9525174409, 323575532569, 10992042930625, 373405884106369, 12684808016683609, 430910066683134025, 14638257459209870929, 497269843546452475249, 16892536423120174285225
Offset: 1
Keywords
Examples
a(3) = 34*a(2)-a(1)-2312 = 34*7225-289-2312 = 243049.
Links
- Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
Crossrefs
Second trisection of A156159.
Equals 289*A008844. - Klaus Brockhaus, Sep 23 2009
Cf. A156164 (decimal expansion of (17+12*sqrt(2))).
Programs
-
Mathematica
RecurrenceTable[{a[1]==289,a[2]==7225,a[n]==34a[n-1]-a[n-2]-2312},a,{n,20}] (* or *) LinearRecurrence[{35,-35,1},{289,7225,243049},20] (* Harvey P. Dale, Dec 11 2013 *) -
PARI
{m=14; v=concat([289, 7225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}
Formula
a(n) = (578+(867-578*sqrt(2))*(17+12*sqrt(2))^n+(867+578*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: x*(289-2890*x+289*x^2)/((1-x)*(1-34*x+x^2)). [corrected by Klaus Brockhaus, Sep 23 2009]
a(1)=289, a(2)=7225, a(3)=243049, a(n) = 35*a(n-1)-35*a(n-2)+a(n-3). - Harvey P. Dale, Dec 11 2013
Comments