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A277131
Magic numbers of anti-Mackay icosahedra.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Felix Fröhlich, Oct 01 2016
STATUS
approved