cp's OEIS Frontend

A212766 Number of (w,x,y,z) with all terms in {0,...,n}, w even and x odd.

%I A212766 #15 Jan 05 2025 05:53:34
%S A212766 0,4,18,64,150,324,588,1024,1620,2500,3630,5184,7098,9604,12600,16384,
%T A212766 20808,26244,32490,40000,48510,58564,69828,82944,97500,114244,132678,
%U A212766 153664,176610,202500,230640,262144,296208,334084,374850
%N A212766 Number of (w,x,y,z) with all terms in {0,...,n}, w even and x odd.
%C A212766 Every term is even.
%C A212766 For a guide to related sequences, see A211795.
%H A212766 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F A212766 a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
%F A212766 G.f.: -2*x*(2+5*x+10*x^2+5*x^3+2*x^4) / ( (1+x)^3*(x-1)^5 ).
%F A212766 a(n) = (2n(n+2)-(-1)^n+1)(n+1)^2/8. [_Bruno Berselli_, Jun 11 2012]
%t A212766 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1), s++], {w, 0, n}, {x, 0,  n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212766 Map[t[#] &, Range[0, 40]]  (* A212766 *)
%t A212766 %/2 (* integers *)
%t A212766 LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 4, 18, 64, 150, 324, 588, 1024}, 40]
%Y A212766 Cf. A211795.
%K A212766 nonn,easy
%O A212766 0,2
%A A212766 _Clark Kimberling_, May 29 2012