A212980 - OEIS

%I #16 Nov 19 2021 12:08:19

%S 0,1,6,17,37,68,113,174,254,355,480,631,811,1022,1267,1548,1868,2229,

%T 2634,3085,3585,4136,4741,5402,6122,6903,7748,8659,9639,10690,11815,

%U 13016,14296,15657,17102,18633,20253,21964,23769,25670,27670

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

%C For a guide to related sequences, see A212959.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

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

%F G.f.: (x + 3*x^2 + x^3)/((1 + x)*(1 - x)^4).

%F From _Ayoub Saber Rguez_, Oct 08 2021: (Start)

%F a(n) = A212981(n) - A002620(n+1).

%F a(n) = (10*n^3 + 15*n^2 + 2*n - 3 + 3*((n+1) mod 2))/24. (End)

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

%t (Do[If[w < x + y && x < y, s = s + 1],

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

%t m = Map[t[#] &, Range[0, 60]]   (* A212980 *)

%Y Cf. A002620, A212981, A212959.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Jun 03 2012