A146965 a(n) = 10*a(n-1) - 18*a(n-2) with a(0)=1, a(1)=5.

1, 5, 32, 230, 1724, 13100, 99968, 763880, 5839376, 44643920, 341330432, 2609713760, 19953189824, 152557050560, 1166413088768, 8918103977600, 68185604178176, 521330170184960, 3985960826642432, 30475665203095040

Offset

0,2

Comments

The Mathematica program implements the formula provided by Deleham and Brockhaus. - Harvey P. Dale, Feb 17 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..145

Index entries for linear recurrences with constant coefficients, signature (10,-18).

Formula

a(n) = ((5 + sqrt(7))^n + (5 - sqrt(7))^n)/2.

G.f.: (1-5*x)/(1-10*x+18*x^2). - Philippe Deléham and Klaus Brockhaus, Nov 05 2008

a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*7^(n-k))/5^n. - Philippe Deléham, Nov 06 2008

E.g.f.: exp(5*x)*cosh(sqrt(7)*x). - G. C. Greubel, Jan 08 2020

Maple

seq(coeff(series((1-5*x)/(1-10*x+18*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 08 2020

Mathematica

Transpose[NestList[{#[[2]], 10#[[2]]-18#[[1]]}&, {1, 5}, 20]][[1]]  (* Harvey P. Dale, Feb 17 2011 *)
LinearRecurrence[{10, -18}, {1, 5}, 30] (* Harvey P. Dale, Aug 27 2013 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((5+r7)^n+(5-r7)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008
(PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+18*x^2)) \\ G. C. Greubel, Jan 08 2020
(Sage)
def A146965_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-5*x)/(1-10*x+18*x^2) ).list()
A146965_list(30) # G. C. Greubel, Jan 08 2020
(GAP) a:=[1, 5];; for n in [3..30] do a[n]:=10*a[n-1]-18*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020

Crossrefs

Sequence in context: A208632 A065071 A153396 * A243693 A364747 A053157

Adjacent sequences: A146962 A146963 A146964 * A146966 A146967 A146968

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008

Extensions

Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008

Name from Philippe Deléham and Klaus Brockhaus, Nov 05 2008

Status

approved