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A008528
Coordination sequence for 4-dimensional RR-centered di-isohexagonal orthogonal lattice.
3
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
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]
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 * A373316 A020881 A285043
KEYWORD
nonn,easy
STATUS
approved