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%I #14 Apr 19 2016 11:10:55
%S 1,2,3,4,8,7,6,5,9,10,11,12,16,15,14,13,17,18,19,20,24,23,22,21,25,26,
%T 27,28,32,31,30,29,33,34,35,36,40,39,38,37,41,42,43,44,48,47,46,45,49,
%U 50,51,52,56,55,54,53,57,58,59,60,64,63,62,61,65,66,67,68,72,71,70,69,73,74,75
%N Expansion of (1 + x + x^2 + x^3 + 4*x^4 - x^5 - x^6 - x^7 + 3*x^8)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)).
%C In each group of 8 consecutive numbers, swap 5 and 8 terms, 6 and 7 terms.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F G.f.: (1 + x + x^2 + x^3 + 4*x^4 - x^5 - x^6 - x^7 + 3*x^8)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)).
%F a(n) = a(n-1) + a(n-8) - a(n-9).
%F a(n) = 1 + n + 3*floor(n/4) - 2*floor((n+1)/8) - 2*floor((n+2)/8) - 2*floor((n+3)/8). - _Vaclav Kotesovec_, Apr 19 2016
%t CoefficientList[Series[(1 + x + x^2 + x^3 + 4 x^4 - x^5 - x^6 - x^7 + 3 x^8)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)), {x, 0, 75}], x]
%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 8, 7, 6, 5, 9}, 75]
%o (PARI) x='x+O('x^99); Vec((1+x+x^2+x^3+4*x^4-x^5-x^6-x^7+3*x^8)/((1-x)^2*(1+x+x^2+x^3 +x^4+x^5+x^6+x^7))) \\ _Altug Alkan_, Apr 18 2016
%Y Cf. A000027, A133256, A133259.
%K nonn,easy
%O 0,2
%A _Ilya Gutkovskiy_, Apr 17 2016
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