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

0,2

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).

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

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 *)

Crossrefs

Sequence in context: A210687 A000739 A186852 * A022708 A328816 A146211

Adjacent sequences: A010076 A010077 A010078 * A010080 A010081 A010082

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Jul 07 2013

Status

approved