A212977 - OEIS

A212977

Number of (w,x,y) with all terms in {0,...,n} and n/2 < w+x+y <= n.

0, 3, 6, 16, 25, 46, 64, 100, 130, 185, 230, 308, 371, 476, 560, 696, 804, 975, 1110, 1320, 1485, 1738, 1936, 2236, 2470, 2821, 3094, 3500, 3815, 4280, 4640, 5168, 5576, 6171, 6630, 7296, 7809, 8550, 9120, 9940, 10570, 11473, 12166, 13156

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OFFSET

0,2

COMMENTS

For a guide to related sequences, see A212959.

LINKS

Table of n, a(n) for n=0..43.

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

FORMULA

a(n)=a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).

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

and g(x)=((1+x)^3)(1-x)^4.

a(n) = (14*n^3+75*n^2+109*n-3*((n^2+7*n+11)*(-1)^n-11))/96. - Luce ETIENNE, Mar 21 2014

MATHEMATICA

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

(Do[If[n/2 < w + x + y <= n, s = s + 1],

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

m = Map[t[#] &, Range[0, 70]] (* A212977 *)

CROSSREFS

Cf. A212959.

Sequence in context: A116613 A291803 A330017 * A127935 A144538 A130596

Adjacent sequences: A212974 A212975 A212976 * A212978 A212979 A212980

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 04 2012

STATUS

approved