A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
1, 8, 68, 600, 5408, 49312, 452416, 4164096, 38391040, 354254336, 3270354944, 30197778432, 278873280512, 2575523676160, 23786907123712, 219693657980928, 2029087298289664, 18740701224894464, 173089976023777280
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-44).
Programs
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Magma
[ n le 2 select 7*n-6 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];
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Mathematica
LinearRecurrence[{14,-44}, {1,8}, 50] (* G. C. Greubel, Dec 18 2016 *) -
PARI
Vec((1-6*x)/(1-14*x+44*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016
Formula
a(n) = ((5+sqrt(5))*(7+sqrt(5))^n + (5-sqrt(5))*(7-sqrt(5))^n)/10.
G.f.: (1-6*x)/(1-14*x+44*x^2).
E.g.f.: (1/5)*exp(7*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016
Comments