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%I #32 Apr 10 2018 08:26:35
%S 1,4,10,21,37,57,81,109,142,180,222,268,318,373,433,497,565,637,714,
%T 796,882,972,1066,1165,1269,1377,1489,1605,1726,1852,1982,2116,2254,
%U 2397,2545,2697,2853,3013,3178,3348,3522,3700,3882,4069,4261,4457,4657,4861
%N Coordination sequence for Paracelsian.
%D Inorganic Crystal Structure Database: Collection Code 24690.
%H Colin Barker, <a href="/A008260/b008260.txt">Table of n, a(n) for n = 0..1000</a>
%H R. W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Coordination Sequences and Encyclopedia of Integer Sequences</a>
%H R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, <a href="http://neilsloane.com/doc/ac96cs/">Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites</a>, Acta Cryst., A52 (1996), pp. 879-889.
%H Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F From _N. J. A. Sloane_, Mar 15 1996: (Start)
%F a(5*k) = 55*k^2 + 2 with k>0 and a(0)=1,
%F a(5*k+1) = 55*k^2 + 22*k + 4,
%F a(5*k+2) = 55*k^2 + 44*k + 10,
%F a(5*k+3) = 55*k^2 + 66*k + 21,
%F a(5*k+4) = 55*k^2 + 88*k + 37. (End)
%F G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 5*x^4 + 3*x^5 + 2*x^6 + x^7)/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)). - _Bruno Berselli_, Jul 24 2013
%F a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n>7. - _Colin Barker_, Feb 15 2018
%t LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 4, 10, 21, 37, 57, 81, 109}, 50] (* _Harvey P. Dale_, Jul 29 2015 *)
%o (PARI) Vec((1 + x)*(1 + x + 2*x^2 + 3*x^3 + 2*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Feb 15 2018
%K nonn,easy
%O 0,2
%A _Ralf W. Grosse-Kunstleve_
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