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A212964 Number of (w,x,y) with all terms in {0,...,n} and |w-x| < |x-y| < |y-w|. 9
0, 0, 0, 2, 6, 14, 26, 44, 68, 100, 140, 190, 250, 322, 406, 504, 616, 744, 888, 1050, 1230, 1430, 1650, 1892, 2156, 2444, 2756, 3094, 3458, 3850, 4270, 4720, 5200, 5712, 6256, 6834, 7446, 8094, 8778, 9500, 10260, 11060, 11900, 12782, 13706 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For a guide to related sequences, see A212959.

Magic numbers of nucleons in a biaxially deformed nucleus at oscillator ratio 1:2 (oblate ellipsoid) under the simple harmonic oscillator model. - Jess Tauber, May 14 2013

a(n) is the number of Sidon subsets of {1,..,n+1} of size 3. - Carl Najafi, Apr 27 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Ikuko Hamamoto, One-particle motion in nuclear many-body problem, Division of Mathematical Physics, LTH, University of Lund, Sweden.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

G.f.: f(x)/g(x), where f(x)=2*x^3 and g(x)=(1+x)(1-x)^4.

a(n+3) = 2*A002623(n).

a(n) = sum(k=0..n, floor((k-1)^2/2))). - Enrique Pérez Herrero, Dec 28 2013

a(n) = sum_{i=1..n} floor(i^2/2) - 2*floor(i/2). - Wesley Ivan Hurt, Jul 23 2014

a(n) = (2*n-1)*(2*n^2-2*n-3)/24 - (-1)^n/8. - Robert Israel, Jul 23 2014

MAPLE

A212964:=n->add(floor(i^2/2) - 2*floor(i/2), i=1..n): seq(A212964(n), n=0..50); # Wesley Ivan Hurt, Jul 23 2014

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[Abs[w - x] < Abs[x - y] < Abs[y - w], s = s + 1],

{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

m = Map[t[#] &, Range[0, 45]]   (* A212964 *)

m/2 (* essentially A002623 *)

CoefficientList[Series[2 x^3/((1 + x) (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 25 2014 *)

PROG

(MAGMA) [(2*n-1)*(2*n^2-2*n-3)/24 - (-1)^n/8: n in [0..50]]; // Vincenzo Librandi, Jul 25 2014

(PARI) a(n) = (2*n-1)*(2*n^2-2*n-3)/24 - (-1)^n/8;

vector (100, n, a(n-1)) \\ Altug Alkan, Sep 30 2015

CROSSREFS

Cf. A212959.

First differences: A007590, is first differences of 2*A001752(n-4) for n > 3; partial sums: 2*A001752(n-3) for n > 2, is partial sums of A007590(n-1) for n > 0. - Guenther Schrack, Mar 19 2018

Sequence in context: A063620 A162716 A138318 * A279742 A068042 A068041

Adjacent sequences:  A212961 A212962 A212963 * A212965 A212966 A212967

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 02 2012

STATUS

approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)