%I #13 Feb 24 2019 09:08:39
%S 1,1,4,5,16,22,29,45,76,126,210,338,534,869,1414,2301,3741,6052,9805,
%T 15910,25820,41900,67966,110226,178791,290044,470524,763285,1238156,
%U 2008452,3258039,5285117,8573382,13907463,22560169,36596300,59365317,96300513
%N a(n) = a(n-1) + a(n-3) + 2*a(n-5) - a(n-8) - a(n-10), n > 10.
%C For n >= 5, gives the dimensions of a certain class of error-correcting codes. [Cascudo, Theorem 6.2]
%H Colin Barker, <a href="/A293344/b293344.txt">Table of n, a(n) for n = 1..1000</a>
%H Ignacio Cascudo, <a href="https://arxiv.org/abs/1703.01267">On squares of cyclic codes</a>, arXiv:1703.01267 [cs.IT], 2017.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,2,0,0,-1,0,-1).
%F G.f.: x*(1 + 3*x^2 + 10*x^4 - 8*x^7 - 10*x^9) / (1 - x - x^3 - 2*x^5 + x^8 + x^10). - _Colin Barker_, Feb 24 2019
%t a = DifferenceRoot[Function[{a, n}, {a[n] + a[n+2] - 2*a[n+5] - a[n+7] - a[n+9] + a[n+10] == 0, a[1] == 1, a[2] == 1, a[3] == 4, a[4] == 5, a[5] == 16, a[6] == 22, a[7] == 29, a[8] == 45, a[9] == 76, a[10] == 126}]];
%t Table[a[n], {n, 1, 38}] (* _Jean-François Alcover_, Feb 24 2019 *)
%o (PARI) Vec(x*(1 + 3*x^2 + 10*x^4 - 8*x^7 - 10*x^9) / (1 - x - x^3 - 2*x^5 + x^8 + x^10) + O(x^40)) \\ _Colin Barker_, Feb 24 2019
%Y Cf. A293343, A293345.
%K nonn,easy
%O 1,3
%A _Eric M. Schmidt_, Oct 12 2017