A010079 Coordination sequence for net formed by holes in D_4 lattice.

1, 16, 104, 344, 792, 1528, 2632, 4152, 6200, 8792, 12072, 16024, 20824, 26424, 33032, 40568, 49272, 59032, 70120, 82392, 96152, 111224, 127944, 146104, 166072, 187608, 211112, 236312, 263640, 292792, 324232, 357624, 393464, 431384, 471912, 514648, 560152

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 sequences related to D_4 lattice
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Programs

Maple

f := n-> if n mod 2 = 0 then 12*n^3+8*n-8 else 12*n^3+4*n+8; fi; #(for n>1).

Mathematica

CoefficientList[Series[-(8 x^7 - 25 x^6 + 2 x^5 - 63 x^4 - 124 x^3 - 71 x^2 - 14 x-1)/((x - 1)^4 (x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{2,1,-4,1,2,-1},{1,16,104,344,792,1528,2632,4152},40] (* Harvey P. Dale, Nov 08 2017 *)

Formula

a(n) = 2*(-4*(-1)^n+(3+(-1)^n)*n+6*n^3) for n>1. G.f.: -(8*x^7 -25*x^6 +2*x^5 -63*x^4 -124*x^3 -71*x^2 -14*x -1) / ((x-1)^4*(x+1)^2). - Colin Barker, Jul 07 2013

Extensions

More terms from Colin Barker, Jul 07 2013