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 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 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). 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 AUTHOR STATUS approved

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Last modified April 15 02:27 EDT 2021. Contains 342974 sequences. (Running on oeis4.)