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A008533 Coordination sequence for {A_5}* lattice.

%I A008533 #28 Sep 08 2022 08:44:36
%S A008533 1,12,72,272,762,1752,3512,6372,10722,17012,25752,37512,52922,72672,
%T A008533 97512,128252,165762,210972,264872,328512,403002,489512,589272,703572,
%U A008533 833762,981252,1147512,1334072,1542522,1774512,2031752,2316012,2629122,2972972,3349512
%N A008533 Coordination sequence for {A_5}* lattice.
%H A008533 Colin Barker, <a href="/A008533/b008533.txt">Table of n, a(n) for n = 0..1000</a>
%H A008533 M. O'Keeffe, <a href="http://dx.doi.org/10.1524/zkri.1995.210.12.905">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908.
%H A008533 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H A008533 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A008533 a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) for n>5. - _Colin Barker_, Mar 03 2015
%F A008533 G.f.: (1+x)*(1+6*x+16*x^2+6*x^3+x^4)/(1-x)^5. - _Colin Barker_, Mar 03 2015
%F A008533 E.g.f.: -1 + (4 + 20*x + 50*x^2 + 30*x^3 + 5*x^4)*exp(x)/2. - _G. C. Greubel_, Nov 10 2019
%p A008533 1, seq( (5*k^4+15*k^2+4)/2, k=1..40);
%t A008533 Table[If[n==0, 1, (4+15*n^2+5*n^4)/2], {n,0,40}] (* _G. C. Greubel_, Nov 10 2019 *)
%t A008533 LinearRecurrence[{5,-10,10,-5,1},{1,12,72,272,762,1752},50] (* _Harvey P. Dale_, Jan 08 2020 *)
%o A008533 (PARI) Vec(-(x+1)*(x^4+6*x^3+16*x^2+6*x+1) / (x-1)^5 + O(x^40)) \\ _Colin Barker_, Mar 03 2015
%o A008533 (PARI) vector(46, n, if(n==1,1, (4 +15*(n-1)^2 +5*(n-1)^4)/2 ) ) \\ _G. C. Greubel_, Nov 10 2019
%o A008533 (Magma) [1] cat [(4+15*n^2+5*n^4)/2: n in [1..45]]; // _G. C. Greubel_, Nov 10 2019
%o A008533 (Sage) [1]+[(4+15*n^2+5*n^4)/2 for n in (1..45)]; # _G. C. Greubel_, Nov 10 2019
%o A008533 (GAP) Concatenation([1], List([1..45], n-> (4+15*n^2+5*n^4)/2 )); # _G. C. Greubel_, Nov 10 2019
%K A008533 nonn,easy
%O A008533 0,2
%A A008533 _N. J. A. Sloane_