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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

GAP

Concatenation([1], List([1..45], n-> n*(7+11*n^2) )); # G. C. Greubel, Nov 09 2019

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

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 *)

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

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