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A010079 Coordination sequence for net formed by holes in D_4 lattice. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified November 20 20:28 EST 2019. Contains 329347 sequences. (Running on oeis4.)