OFFSET
0,2
LINKS
Matthew House, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-23).
FORMULA
a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
a(n) = ((1+sqrt(2))*(5+sqrt(2))^n + (1-sqrt(2))*(5-sqrt(2))^n)/2.
G.f.: (1-3*x)/(1-10*x+23*x^2).
E.g.f.: (sqrt(2)*sinh(sqrt(2)*x) + cosh(sqrt(2)*x))*exp(5*x). - Ilya Gutkovskiy, Jun 30 2016
MATHEMATICA
CoefficientList[Series[(1 - 3 x)/(1 - 10 x + 23 x^2), {x, 0, 21}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{10, -23}, {1, 7}, 50] (* G. C. Greubel, Dec 19 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-3*x)/(1-10*x+23*x^2) + O(x^99)) \\ Altug Alkan, Jul 05 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009
New name from G. C. Greubel, Dec 19 2016
STATUS
approved