A146962 a(n) = 10*a(n-1) - 19*a(n-2) with a(0)=1, a(1)=5.
1, 5, 31, 215, 1561, 11525, 85591, 636935, 4743121, 35329445, 263175151, 1960492055, 14604592681, 108796577765, 810478516711, 6037650189575, 44977410078241, 335058747180485, 2496016680318271, 18594050606753495
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-19).
Programs
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GAP
a:=[1,5];; for n in [3..30] do a[n]:=10*a[n-1]-19*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020
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Magma
Z
:= PolynomialRing(Integers()); N :=NumberField(x^2-6); S:=[ ((5+r6)^n+(5-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008 -
Maple
seq(coeff(series((1-5*x)/(1-10*x+19*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 08 2020
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Mathematica
LinearRecurrence[{10,-19},{1,5},30] (* Harvey P. Dale, Apr 27 2014 *) CoefficientList[Series[(1-5x)/(1-10x+19x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2014 *) -
PARI
my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+19*x^2)) \\ G. C. Greubel, Jan 08 2020 -
Sage
def A146962_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( (1-5*x)/(1-10*x+19*x^2) ).list() A146962_list(30) # G. C. Greubel, Jan 08 2020
Formula
a(n) = ((5 + sqrt(6))^n + (5 - sqrt(6))^n)/2.
G.f.: (1-5*x)/(1-10*x+19*x^2). - Philippe Deléham and Klaus Brockhaus, Nov 05 2008
a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*6^(n-k))/5^n. - Philippe Deléham, Nov 06 2008
E.g.f.: exp(5*x)*cosh(sqrt(6)*x). - G. C. Greubel, Jan 08 2020
Extensions
Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008
Edited by Klaus Brockhaus, Jul 15 2009
Name from Philippe Deléham and Klaus Brockhaus, Nov 05 2008
Comments