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

Author

Felix Fröhlich, Oct 01 2016

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A005902, A008592, A018226, A018227.

Programs

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 *)

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

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)