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A266084 Expansion of (5 - x - x^2 - x^3 - x^4 + 4*x^5)/( x^6 - x^5 - x + 1).

%I A266084 #37 Feb 16 2025 08:33:28
%S A266084 5,4,3,2,1,10,9,8,7,6,15,14,13,12,11,20,19,18,17,16,25,24,23,22,21,30,
%T A266084 29,28,27,26,35,34,33,32,31,40,39,38,37,36,45,44,43,42,41,50,49,48,47,
%U A266084 46,55,54,53,52,51,60,59,58,57,56,65,64,63,62,61,70
%N A266084 Expansion of (5 - x - x^2 - x^3 - x^4 + 4*x^5)/( x^6 - x^5 - x + 1).
%C A266084 Invert blocks of five in the sequence of natural numbers.
%H A266084 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NaturalNumber.html">Natural Number</a>
%H A266084 <a href="/index/Per#IntegerPermutation">Index entries for permutations of the positive (or nonnegative) integers</a>.
%H A266084 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A266084 G.f.: (5 - x - x^2 - x^3 - x^4 + 4*x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
%F A266084 a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.
%F A266084 a(n) = 5 + 5*floor(n/5) - n mod 5.
%F A266084 a(n) = n+1+2*A257145(n+3). - _R. J. Mathar_, Apr 12 2019
%t A266084 Table[5 + 5 Floor[n/5] - Mod[n, 5], {n, 0, 50}]
%t A266084 CoefficientList[Series[(5 - x - x^2 - x^3 - x^4 + 4 x^5)/(x^6 - x^5 - x + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 21 2015 *)
%t A266084 Reverse/@Partition[Range[80],5]//Flatten (* or *) LinearRecurrence[ {1,0,0,0,1,-1},{5,4,3,2,1,10},80] (* _Harvey P. Dale_, Sep 02 2016 *)
%o A266084 (Magma) [5+5*Floor(n/5)-n mod 5: n in [0..70]]; // _Vincenzo Librandi_, Dec 21 2015
%o A266084 (PARI) a(n) = 5 + 5*(n\5) - (n % 5); \\ _Michel Marcus_, Dec 21 2015
%o A266084 (PARI) x='x+O('x^100); Vec((5-x-x^2-x^3-x^4+4*x^5)/(x^6-x^5-x+1)) \\ _Altug Alkan_, Dec 21 2015
%Y A266084 Cf. A000027, A113655, A113778.
%K A266084 nonn,easy
%O A266084 0,1
%A A266084 _Ilya Gutkovskiy_, Dec 21 2015