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%I #23 Sep 08 2022 08:45:38
%S 1,5,31,215,1561,11525,85591,636935,4743121,35329445,263175151,
%T 1960492055,14604592681,108796577765,810478516711,6037650189575,
%U 44977410078241,335058747180485,2496016680318271,18594050606753495
%N a(n) = 10*a(n-1) - 19*a(n-2) with a(0)=1, a(1)=5.
%C Binomial transform of A143648.
%C Inverse binomial transform of A145301.
%H Vincenzo Librandi, <a href="/A146962/b146962.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-19).
%F a(n) = ((5 + sqrt(6))^n + (5 - sqrt(6))^n)/2.
%F G.f.: (1-5*x)/(1-10*x+19*x^2). - _Philippe Deléham_ and _Klaus Brockhaus_, Nov 05 2008
%F a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*6^(n-k))/5^n. - _Philippe Deléham_, Nov 06 2008
%F E.g.f.: exp(5*x)*cosh(sqrt(6)*x). - _G. C. Greubel_, Jan 08 2020
%p 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
%t LinearRecurrence[{10,-19},{1,5},30] (* _Harvey P. Dale_, Apr 27 2014 *)
%t CoefficientList[Series[(1-5x)/(1-10x+19x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=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
%o (PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+19*x^2)) \\ _G. C. Greubel_, Jan 08 2020
%o (Sage)
%o def A146962_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-5*x)/(1-10*x+19*x^2) ).list()
%o A146962_list(30) # _G. C. Greubel_, Jan 08 2020
%o (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
%Y Cf. A098158, A143648, A145301.
%K nonn,easy
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
%E Extended beyond a(7) by _Klaus Brockhaus_, Nov 05 2008
%E Edited by _Klaus Brockhaus_, Jul 15 2009
%E Name from _Philippe Deléham_ and _Klaus Brockhaus_, Nov 05 2008
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