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A225566
The set of magic numbers for an idealized harmonic oscillator atomic nucleus with a biaxially deformed prolate ellipsoid shape and an oscillator ratio of 3:1
1
2, 4, 6, 12, 18, 24, 36, 48, 60, 80, 100, 120, 150, 180, 210, 252, 294, 336, 392, 448, 504, 576, 648, 720, 810, 900, 990, 1100, 1210, 1320, 1452, 1584, 1716, 1872, 2028, 2184, 2366, 2548, 2730, 2940, 3150, 3360, 3600, 3840, 4080, 4352, 4624, 4896, 5202, 5508, 5814, 6156, 6498, 6840, 7220, 7600, 7980, 8400, 8820, 9240, 9702
OFFSET
1,1
COMMENTS
Partial sums of series of three doubled triangular numbers of the same value in order: 2,2,2,6,6,6,12,12,12,20,20,20... (cf. A002378).
FORMULA
From Colin Barker, Oct 01 2016: (Start)
a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8) for n>8.
G.f.: 2*x / ((1-x)^4*(1+x+x^2)^2).
(End)
MATHEMATICA
Accumulate[Flatten[{#, #, #}&/@Accumulate[2*Range[30]]]] (* Harvey P. Dale, May 01 2014 *)
PROG
(PARI) Vec(2*x/((1-x)^4*(1+x+x^2)^2) + O(x^60)) \\ Colin Barker, Oct 01 2016
CROSSREFS
Equals twice A144677. Cf. A002378.
Sequence in context: A171923 A060735 A181416 * A273009 A051683 A215821
KEYWORD
nonn,easy
AUTHOR
Jess Tauber, May 14 2013
EXTENSIONS
More terms from N. J. A. Sloane, May 17 2013
STATUS
approved