OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
G. Nebe and N. J. A. Sloane, Home page for this lattice
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 (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: (1+x)*(1+8*x+29*x^2+64*x^3+29*x^4+8*x^5+x^6)/(1-x)^7. - Colin Barker, Mar 03 2015
E.g.f.: -1 + (36 + 252*x + 882*x^2 + 1050*x^3 + 525*x^4 + 105*x^5 + 7*x^6)*exp(x)/18. - G. C. Greubel, Nov 10 2019
MAPLE
1, seq( (7*k^6+70*k^4+175*k^2+36)/18, k=1..40);
MATHEMATICA
Table[If[n==0, 1, (36+175*n^2+70*n^4+7*n^6)/18], {n, 0, 40}] (* G. C. Greubel, Nov 10 2019 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 16, 128, 688, 2746, 8752, 23536, 55568}, 40] (* Harvey P. Dale, Jun 04 2023 *)
PROG
(PARI) Vec(-(x+1)*(x^6+8*x^5+29*x^4+64*x^3+29*x^2+8*x+1) / (x-1)^7 + O(x^40)) \\ Colin Barker, Mar 03 2015
(PARI) vector(46, n, if(n==1, 1, (36+175*(n-1)^2+70*(n-1)^4+7*(n-1)^6)/18 ) ) \\ G. C. Greubel, Nov 10 2019
(Magma) [1] cat [(36+175*n^2+70*n^4+7*n^6)/18: n in [1..45]]; // G. C. Greubel, Nov 10 2019
(Sage) [1]+[(36+175*n^2+70*n^4+7*n^6)/18 for n in (1..45)]; # G. C. Greubel, Nov 10 2019
(GAP) Concatenation([1], List([1..45], n-> (36+175*n^2+70*n^4+7*n^6)/18 )); # G. C. Greubel, Nov 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved