A277131 Magic numbers of anti-Mackay icosahedra.

45, 127, 279, 521, 873, 1355, 1987, 2789, 3781, 4983, 6415, 8097, 10049, 12291, 14843, 17725, 20957, 24559, 28551, 32953, 37785, 43067, 48819, 55061, 61813, 69095, 76927, 85329, 94321, 103923, 114155, 125037, 136589, 148831, 161783, 175465, 189897, 205099

Offset

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..1000

D. Bochicchio and R. Ferrando, Size-Dependent Transition to High-Symmetry Chiral Structures in AgCu, AgCo, AgNi, and AuNi Nanoalloys, Nano Letters, Vol. 10, No. 10 (2010), 4211-4216.

Index entries for sequences related to magic numbers

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = A005902(n) - A008592(n-1).

a(n) = 10/3*n^3 + 25*n^2 + 161/3*n + 45 with offset 0.

From Colin Barker, Oct 01 2016: (Start)

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>5.

a(n) = 11-(19*n)/3+5*n^2+(10*n^3)/3.

G.f.: x^2*(45-53*x+41*x^2-13*x^3) / (1-x)^4.

(End)

Maple

A277131:=n->11-(19*n)/3+5*n^2+(10*n^3)/3: seq(A277131(n), n=2..50); # Wesley Ivan Hurt, Oct 07 2016

Mathematica

DeleteCases[CoefficientList[Series[x^2*(45 - 53 x + 41 x^2 - 13 x^3)/(1 - x)^4, {x, 0, 39}], x], 0] (* Michael De Vlieger, Oct 02 2016 *)

Prog

(PARI) a(n) = (2*n+1) * (5*n^2+5*n+3) / 3 - 10*(n-1)
(PARI) Vec(x^2*(45-53*x+41*x^2-13*x^3)/(1-x)^4 + O(x^50)) \\ Colin Barker, Oct 01 2016

Crossrefs

Cf. A005902, A008592, A018226, A018227.

Sequence in context: A140369 A044296 A044677 * A206209 A098924 A195318

Adjacent sequences: A277128 A277129 A277130 * A277132 A277133 A277134

Keyword

nonn,easy

Author

Felix Fröhlich, Oct 01 2016

Status

approved