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%I A011906 #30 Oct 18 2024 06:08:52
%S A011906 1,18,525,17340,586177,19896030,675781821,22956120408,779829016225,
%T A011906 26491211221770,899921240562957,30570830315362260,1038508305678375841,
%U A011906 35278711540581704598,1198437683944896688125,40711602541832856049200,1382996048733983114022337
%N A011906 If b(n) is A011900(n) and c(n) is A001109(n), then a(n) = b(n)*c(n) = b(n) + (b(n)+1) + (b(n)+2) + ... + c(n).
%D A011906 Mario Velucchi "From the desk of ... Mario Velucchi" in 'Mathematics and Informatics quarterly' volume 7 - 2/1997, p. 81.
%H A011906 G. C. Greubel, <a href="/A011906/b011906.txt">Table of n, a(n) for n = 1..650</a>
%H A011906 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (41,-246,246,-41,1).
%F A011906 From _R. J. Mathar_, Apr 15 2010: (Start)
%F A011906 G.f.: x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)).
%F A011906 a(n) = 41*a(n-1) -246*a(n-2) +246*a(n-3) -41*a(n-4) +a(n-5). (End)
%F A011906 Lim_{n -> infinity} a(n)/a(n-1) = A156164. - _César Aguilera_, Jul 17 2020
%F A011906 a(n) = (1/16)*(1 - A029547(n) + 41*A091761(n) + 8*A001109(n)). - _G. C. Greubel_, Oct 18 2024
%e A011906 a(3) = 525 = 15*35 = 15 + 16 + ... + 35.
%p A011906 A011900 := proc(n) coeftayl( (1-4*x+x^2)/((1-x)*(1-6*x+x^2)),x=0,n) ; end proc: A001109 := proc(n) coeftayl( x/(1-6*x+x^2),x=0,n) ; end proc: A011906 := proc(n) A001109(n)*A011900(n-1) ; end proc: seq(A011906(n),n=1..30) ; # _R. J. Mathar_, Apr 15 2010
%t A011906 LinearRecurrence[{41, -246, 246, -41, 1}, {1, 18, 525, 17340, 586177}, 20] (* _Paul Cleary_, Dec 05 2015 *)
%t A011906 CoefficientList[Series[(-1 + 23*x - 33*x^2 + 3*x^3)/((x - 1)*(x^2 - 34*x + 1)*(1 - 6*x + x^2)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Sep 16 2017 *)
%o A011906 (Magma)
%o A011906 R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)) )); // _G. C. Greubel_, Oct 18 2024
%o A011906 (SageMath)
%o A011906 def A011906_list(prec):
%o A011906     P.<x> = PowerSeriesRing(ZZ, prec)
%o A011906     return P( x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)) ).list()
%o A011906 a=A011906_list(30); a[1:] # _G. C. Greubel_, Oct 18 2024
%Y A011906 Cf. A001109, A011900, A029547, A091761.
%K A011906 nonn,easy
%O A011906 1,2
%A A011906 Mario Velucchi (mathchess(AT)velucchi.it)
%E A011906 More terms from _R. J. Mathar_, Apr 15 2010

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