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%I #34 Dec 10 2023 16:10:37
%S 1,18,102,318,732,1410,2418,3822,5688,8082,11070,14718,19092,24258,
%T 30282,37230,45168,54162,64278,75582,88140,102018,117282,133998,
%U 152232,172050,193518,216702,241668,268482,297210,327918,360672,395538,432582,471870,513468,557442,603858,652782,704280
%N Coordination sequence for 4-dimensional RR-centered di-isohexagonal orthogonal lattice.
%D M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
%H Vincenzo Librandi, <a href="/A008528/b008528.txt">Table of n, a(n) for n = 0..1000</a>
%H 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 M. O'Keeffe, <a href="/A008527/a008527.pdf">Coordination sequences for lattices</a>, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = n*(11*n^2 + 7) with n>0, with a(0)=1.
%F G.f.: 1 + 6*x*(3 + 5*x + 3*x^2)/(1-x)^4. - _R. J. Mathar_, Sep 04 2011
%F E.g.f.: 1 + x*(18 + 33*x + 11*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p 1, seq(11*k^3+7*k, k=1..45);
%t CoefficientList[Series[1+6*x*(3+5*x+3*x^2)/(1-x)^4,{x,0,45}],x] (* _Vincenzo Librandi_, Jun 19 2012 *)
%t LinearRecurrence[{4,-6,4,-1},{1,18,102,318,732},45] (* _Harvey P. Dale_, Apr 27 2017 *)
%o (Magma) I:=[1, 18, 102, 318,732]; [n le 5 select I[n] else 4*Self(n-1) -6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // _Vincenzo Librandi_, Jun 19 2012
%o (PARI) vector(46, n, if(n==1,1,(n-1)*(7+11*(n-1)^2)) ) \\ _G. C. Greubel_, Nov 09 2019
%o (Sage) [1]+[n*(7+11*n^2) for n in (1..45)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) Concatenation([1], List([1..45], n-> n*(7+11*n^2) )); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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