A033547 Otto Haxel's guess for magic numbers of nuclear shells.
0, 2, 6, 14, 28, 50, 82, 126, 184, 258, 350, 462, 596, 754, 938, 1150, 1392, 1666, 1974, 2318, 2700, 3122, 3586, 4094, 4648, 5250, 5902, 6606, 7364, 8178, 9050, 9982, 10976, 12034, 13158, 14350, 15612, 16946, 18354, 19838, 21400, 23042, 24766, 26574, 28468
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- O. Haxel, Die Entstehung des Schalenmodells der Atomkerne, Physikalische Blätter, vol. 50, p. 339, 1994.
- O. Haxel et al., On the "Magic Numbers" in Nuclear Structure, Phys. Rev., 75 (1949), 1766.
- V. Ladma, Magic Numbers
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Programs
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GAP
List([0..50], n-> n*(n^2+5)/3); # G. C. Greubel, Oct 12 2019
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Magma
[n*(n^2+5)/3 : n in [0..50]]; // Wesley Ivan Hurt, Apr 05 2015
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Maple
A033547:=n->n*(n^2+5)/3: seq(A033547(n), n=0..50); # Wesley Ivan Hurt, Apr 05 2015
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Mathematica
Table[n(n^2+5)/3, {n,0,50}] (* Harvey P. Dale, Apr 07 2011 *) LinearRecurrence[{4, -6, 4, -1}, {0, 2, 6, 14}, 50] (* Vincenzo Librandi, Apr 06 2015 *) -
PARI
a(n)=n*(n^2+5)/3 \\ Charles R Greathouse IV, Jun 25 2017
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Sage
[n*(n^2+5)/3 for n in range(50)] # G. C. Greubel, Oct 12 2019
Formula
a(n) = n*(n^2 + 5)/3.
G.f.: 2*x*(1 - x + x^2)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Apr 05 2015
E.g.f.: x*(6 + 3*x + x^2)*exp(x)/3. - G. C. Greubel, Oct 12 2019
a(n) = A046127(n+1) - 2. - Jianing Song, Feb 03 2024
Comments