A008535 Coordination sequence for {A_7}* lattice.

1, 16, 128, 688, 2746, 8752, 23536, 55568, 118498, 232976, 428752, 747056, 1243258, 1989808, 3079456, 4628752, 6781826, 9714448, 13638368, 18805936, 25515002, 34114096, 45007888, 58662928, 75613666, 96468752, 121917616, 152737328, 189799738, 234078896

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

GAP

Concatenation([1], List([1..45], n-> (36+175*n^2+70*n^4+7*n^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

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 *)

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

Sage

[1]+[(36+175*n^2+70*n^4+7*n^6)/18 for n in (1..45)]; # G. C. Greubel, Nov 10 2019

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