|
%I #21 Sep 08 2022 08:45:06
%S 9,1,1,25,25,1,121,225,9,529,1681,441,1849,11025,6889,4225,64009,
%T 73441,2209,326041,632025,31329,1413721,4669921,1320201,4844401,
%U 30371121,19882681,10582009,174847729,208196041,4190209,882030601,1770810561
%N a(n) = A073145(n)^2.
%H Vincenzo Librandi, <a href="/A073702/b073702.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,6,3,2,-1).
%F a(n) = -a(n-2) + 6*a(n-3) + 3*a(n-4) + 2*a(n-5) - a(n-6) with a(0)=9, a(1)=1, a(2)=1, a(3)=25, a(4)=25, a(5)=1.
%F G.f.: (9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6).
%F a(n) = 2*A001644(n) + A073496(n).
%t CoefficientList[Series[(9+x+10x^2-28x^3-7x^4-x^5)/(1+x^2-6x^3-3x^4-2x^5 +x^6), {x, 0, 40}], x]
%t LinearRecurrence[{0,-1,6,3,2,-1},{9,1,1,25,25,1},40] (* _Harvey P. Dale_, Feb 14 2015 *)
%o (PARI) my(x='x+O('x^40)); Vec((9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3 -3*x^4-2*x^5+x^6)) \\ _G. C. Greubel_, Apr 23 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (9+x+ 10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6) )); // _G. C. Greubel_, Apr 23 2019
%o (Sage) ((9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6) ).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 23 2019
%Y Cf. A001644, A073145, A073496.
%K nonn,easy
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Aug 04 2002
|
