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A290986 Expansion of x^6/((1 - x)^2*(1 - 2*x + x^3 - x^4)).

%I A290986 #22 Apr 13 2023 15:34:20
%S A290986 1,4,11,25,52,103,199,379,716,1346,2523,4721,8825,16487,30791,57494,
%T A290986 107343,200400,374116,698403,1303770,2433846,4543428,8481513,15832975,
%U A290986 29556394,55174730,102998026,192272662,358927018,670030771
%N A290986 Expansion of x^6/((1 - x)^2*(1 - 2*x + x^3 - x^4)).
%H A290986 Robert Israel, <a href="/A290986/b290986.txt">Table of n, a(n) for n = 6..3688</a>
%H A290986 T. Langley, J. Liese, and J. Remmel, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Langley/langley2.html">Generating Functions for Wilf Equivalence Under Generalized Factor Order</a>, J. Int. Seq. 14 (2011) # 11.4.2.
%H A290986 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,3,-3,1).
%F A290986 a(n) = A049858(n-2) - (n-2).
%p A290986 f:= gfun:-rectoproc({a(n)-a(n+1)+2*a(n+3)-a(n+4)+n-1, a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 0, a(4) = 0, a(5) = 0, a(6) = 1}, a(n), remember):
%p A290986 map(f, [$6..100]); # _Robert Israel_, Aug 17 2017
%t A290986  LinearRecurrence[{4,-5,1,3,-3,1}, {1,4,11,25,52,103}, 40] (* _Vincenzo Librandi_, Aug 17 2017 *)
%o A290986 (PARI) Vec(x^6/((1-x)^2*(1-2*x+x^3-x^4)) + O(x^50)) \\ _Michel Marcus_, Aug 17 2017
%o A290986 (Magma) I:=[1,4,11,25,52,103]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2)+Self(n-3)+3*Self(n-4)-3*Self(n-5)+Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Aug 17 2017
%o A290986 (SageMath)
%o A290986 def A290986_list(prec):
%o A290986     P.<x> = PowerSeriesRing(ZZ, prec)
%o A290986     return P( x^6/((1-x)^2*(1-2*x+x^3-x^4)) ).list()
%o A290986 a=A290986_list(50); a[6:] # _G. C. Greubel_, Apr 12 2023
%Y A290986 Cf. A049858, A290987, A290989.
%K A290986 nonn,easy
%O A290986 6,2
%A A290986 _R. J. Mathar_, Aug 16 2017