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A082290 Expansion of (1+x+x^2)/((1+x^2)*(1+x)^4*(1-x)^5).

%I A082290 #25 Oct 01 2023 13:43:58
%S A082290 1,2,6,9,19,26,46,59,94,116,172,206,290,340,460,530,695,790,1010,1135,
%T A082290 1421,1582,1946,2149,2604,2856,3416,3724,4404,4776,5592,6036,7005,
%U A082290 7530,8670,9285,10615,11330,12870,13695,15466,16412,18436,19514,21814,23036
%N A082290 Expansion of (1+x+x^2)/((1+x^2)*(1+x)^4*(1-x)^5).
%H A082290 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%H A082290 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -3, -2, 2, -2, 2, 3, -3, -1, 1).
%F A082290 Euler transform of length 4 sequence [ 2, 3, -1, 1]. - _Michael Somos_, Feb 15 2006
%F A082290 G.f.: (1 + x + x^2) / ((1 + x^2) * (1 + x)^4 * (1 - x)^5).
%F A082290 a(n) = 3*a(n-2) - 2*a(n-4) - 2*a(n-6) + 3*a(n-8) - a(n-10) + 3.
%F A082290 a(n) = a(-9-n) for all n in Z.
%F A082290 a(2*n) = A070893(n+1). a(2*n + 1) = A082289(n+4).
%F A082290 a(n) = (6*n^4+108*n^3+666*n^2+1620*n+1251+(4*n^3+54*n^2+236*n+333)*(-1)^n-48*(-1)^((6*n-1+(-1)^n)/4))/1536. - _Luce ETIENNE_, Oct 23 2014
%e A082290 G.f. = 1 + 2*x + 6*x^2 + 9*x^3 + 19*x^4 + 26*x^5 + 46*x^6 + 59*x^7 + ...
%t A082290 Table[(6 n^4 + 108 n^3 + 666 n^2 + 1620 n + 1251 + (4 n^3 + 54 n^2 + 236 n + 333) (-1)^n - 48 (-1)^((6 n - 1 + (-1)^n)/4))/1536, {n, 0, 50}] (* after Luce ETIENNE; or, by definition: *) CoefficientList[Series[(1 + x + x^2)/((1 + x^2)*(1 + x)^4*(1 - x)^5), {x, 0, 50}], x] (* _Bruno Berselli_, Oct 26 2014 *)
%o A082290 (PARI) {a(n) = if( n<-8, a(-9-n), polcoeff( (1 + x + x^2) / ((1 + x^2) *(1 + x)^4 * (1 - x)^5) + x * O(x^n), n))};
%o A082290 (Magma) [(6*n^4 +108*n^3 +666*n^2 +1620*n +1251 +(4*n^3 +54*n^2 +236*n +333)*(-1)^n -48*(-1)^Floor((6*n -1 +(-1)^n)/4))/1536: n in [0..50]]; // _Vincenzo Librandi_, Oct 23 2014
%Y A082290 Cf. A070893, A082289.
%K A082290 nonn,easy
%O A082290 0,2
%A A082290 _Michael Somos_, Apr 07 2003