A066394 Coordination sequence for ReO_3 net with respect to oxygen atom O_1.

1, 2, 10, 10, 46, 26, 106, 50, 190, 82, 298, 122, 430, 170, 586, 226, 766, 290, 970, 362, 1198, 442, 1450, 530, 1726, 626, 2026, 730, 2350, 842, 2698, 962, 3070, 1090, 3466, 1226, 3886, 1370, 4330, 1522, 4798, 1682, 5290, 1850, 5806, 2026, 6346, 2210, 6910

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Jean-Guillaume Eon, Algebraic determination of generating functions for coordination sequences in crystal structures, Acta Cryst. A58 (2002), 47-53.

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

G.f.: (1 + 2*x + 7*x^2 + 4*x^3 + 19*x^4 + 2*x^5 - 3*x^6) / (1 - x^2)^3.

From Colin Barker, Feb 13 2018: (Start)

a(n) = 3*n^2 - 2 for n>0 and even.

a(n) = n^2 + 1 for n odd.

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.

(End)

Prog

(PARI) Vec((1 + 2*x + 7*x^2 + 4*x^3 + 19*x^4 + 2*x^5 - 3*x^6) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 13 2018

Crossrefs

Cf. A066714.

Sequence in context: A156780 A206486 A067046 * A232500 A351659 A033466

Adjacent sequences: A066391 A066392 A066393 * A066395 A066396 A066397

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 24 2001

Status

approved