A008528 Coordination sequence for 4-dimensional RR-centered di-isohexagonal orthogonal lattice.

1, 18, 102, 318, 732, 1410, 2418, 3822, 5688, 8082, 11070, 14718, 19092, 24258, 30282, 37230, 45168, 54162, 64278, 75582, 88140, 102018, 117282, 133998, 152232, 172050, 193518, 216702, 241668, 268482, 297210, 327918, 360672, 395538, 432582, 471870, 513468, 557442, 603858, 652782, 704280

Offset

0,2

References

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = n*(11*n^2 + 7) with n>0, with a(0)=1.

G.f.: 1 + 6*x*(3 + 5*x + 3*x^2)/(1-x)^4. - R. J. Mathar, Sep 04 2011

E.g.f.: 1 + x*(18 + 33*x + 11*x^2)*exp(x). - G. C. Greubel, Nov 09 2019

Maple

1, seq(11*k^3+7*k, k=1..45);

Mathematica

CoefficientList[Series[1+6*x*(3+5*x+3*x^2)/(1-x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Jun 19 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 18, 102, 318, 732}, 45] (* Harvey P. Dale, Apr 27 2017 *)

Prog

(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
(PARI) vector(46, n, if(n==1, 1, (n-1)*(7+11*(n-1)^2)) ) \\ G. C. Greubel, Nov 09 2019
(Sage) [1]+[n*(7+11*n^2) for n in (1..45)] # G. C. Greubel, Nov 09 2019
(GAP) Concatenation([1], List([1..45], n-> n*(7+11*n^2) )); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A107600 A229326 A365107 * A020881 A285043 A223241

Adjacent sequences: A008525 A008526 A008527 * A008529 A008530 A008531

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved