A177422 a(n) = 6*a(n-1)-8*a(n-2) for n > 10; a(0)=221, a(1)=1938, a(2)=8673, a(3)=73729, a(4)=589855, a(5)=7561526, a(6)=34593784, a(7)=218391421, a(8)=2116566392, a(9)=8522858480, a(10)=34225586144.
221, 1938, 8673, 73729, 589855, 7561526, 34593784, 218391421, 2116566392, 8522858480, 34225586144, 137170649024, 549219204992, 2197950037760, 8793946586624, 35180079217664, 140728902612992, 562932781936640
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6, -8).
Programs
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Magma
[221, 1938, 8673, 73729, 589855, 7561526, 34593784, 218391421, 2116566392] cat [2*4^(n+7)-4192257*2^(n-5): n in [9..25]]; // Vincenzo Librandi, Sep 24 2013
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Mathematica
CoefficientList[Series[(221 + 612 x - 1187 x^2 + 37195 x^3 + 216865 x^4 + 4612228 x^5 - 6056532 x^6 + 71320925 x^7 + 1082968138 x^8 - 2429408504 x^9 + 20966400 x^10)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *) -
PARI
{m=18; v=concat([221, 1938, 8673, 73729, 589855, 7561526, 34593784, 218391421, 2116566392, 8522858480, 34225586144], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]); v}
Formula
a(n) = 2*4^(n+7)-4192257*2^(n-5) for n > 8.
G.f.: (221+612*x-1187*x^2+37195*x^3+216865*x^4+4612228*x^5-6056532*x^6 +71320925*x^7+1082968138*x^8-2429408504*x^9+20966400*x^10) / ((1-2*x)*(1-4*x)).
G.f. for the sequence starting at a(9): 16*x^9*(532678655-1056972796*x)/((1-2*x)*(1-4*x)).
Comments