login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033547 Otto Haxel's guess for magic numbers of nuclear shells. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

O. Haxel gave a construction procedure. The formulas are due to Wolfdieter Lang.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

O. Haxel, Die Entstehung des Schalenmodells der Atomkerne, Physikalische Bl├Ątter, 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).

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

MAPLE

A033547:=n->n*(n^2+5)/3: seq(A033547(n), n=0..50); # Wesley Ivan Hurt, Apr 05 2015

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 *)

PROG

(MAGMA) [n*(n^2+5)/3 : n in [0..50]]; // Wesley Ivan Hurt, Apr 05 2015

(PARI) a(n)=n*(n^2+5)/3 \\ Charles R Greathouse IV, Jun 25 2017

(Sage) [n*(n^2+5)/3 for n in range(50)] # G. C. Greubel, Oct 12 2019

(GAP) List([0..50], n-> n*(n^2+5)/3); # G. C. Greubel, Oct 12 2019

CROSSREFS

Equals 2*A004006, partial sums of A014206, 2*(partial sums of A000124).

Cf. A018226.

Sequence in context: A161212 A256058 A294867 * A050531 A290699 A027083

Adjacent sequences:  A033544 A033545 A033546 * A033548 A033549 A033550

KEYWORD

easy,nonn,nice,changed

AUTHOR

Wolfdieter Lang

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 13:38 EDT 2019. Contains 328030 sequences. (Running on oeis4.)