cp's OEIS Frontend

A212965 Number of triples (w,x,y) with all terms in {0,...,n} and such that w = max(w,x,y) - min(w,x,y).

%I A212965 #32 Jan 27 2022 21:25:52
%S A212965 1,4,12,21,37,52,76,97,129,156,196,229,277,316,372,417,481,532,604,
%T A212965 661,741,804,892,961,1057,1132,1236,1317,1429,1516,1636,1729,1857,
%U A212965 1956,2092,2197,2341,2452,2604,2721,2881,3004,3172,3301,3477,3612
%N A212965 Number of triples (w,x,y) with all terms in {0,...,n} and such that w = max(w,x,y) - min(w,x,y).
%C A212965 For a guide to related sequences, see A212959.
%H A212965 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A212965 a(n) = (14*n*(n+1) + (2*n+1)*(-1)^n + 7)/8.
%F A212965 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A212965 G.f.: (1 + 3*x + 6*x^2 + 3*x^3 + x^4)/((1 + x)^2*(1 - x)^3).
%F A212965 From _Ayoub Saber Rguez_, Dec 06 2021: (Start)
%F A212965 a(n) + A213498(n) = (n+1)^3.
%F A212965 a(n) = (7*n^2 + 8*n + 4 - (2*n+1)*(n mod 2))/4. (End)
%t A212965 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212965 (Do[If[w == Max[w, x, y] - Min[w, x, y], s = s + 1],
%t A212965 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212965 Map[t[#] &, Range[0, 50]]   (* A212965 *)
%Y A212965 Cf. A212959, A213498.
%K A212965 nonn,easy
%O A212965 0,2
%A A212965 _Clark Kimberling_, Jun 02 2012