A212765 Number of (w,x,y,z) with all terms in {0,...,n}, w even and x, y, and z odd.

0, 1, 2, 16, 24, 81, 108, 256, 320, 625, 750, 1296, 1512, 2401, 2744, 4096, 4608, 6561, 7290, 10000, 11000, 14641, 15972, 20736, 22464, 28561, 30758, 38416, 41160, 50625, 54000, 65536, 69632, 83521, 88434, 104976, 110808, 130321, 137180

Offset: 0

Author

Clark Kimberling, May 29 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1) && (Mod[y, 2] == 1) && (Mod[z, 2] == 1), s++], {w, 0, n}, {x, 0, n},
{y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]  (* A212765 *)
LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 1, 2, 16, 24, 81, 108, 256, 320}, 40]

Formula

a(n)=a(n-1)+4*a(n-2)-4*a(n-3)-6*a(n-4)+6*a(n-5)+4*a(n-6)-4*a(n-7)-a(n-8)+a(n-9).

G.f.: x*(1+x+10*x^2+7*x^4+x^5+4*x^3) / ( (1+x)^4*(1-x)^5 ).

a(n)=((2*n^4+6*n^3+6*n^2+4*n+1)-(2*n^3+6*n^2+4*n+1)*(-1)^n)/32. - Luce ETIENNE, Apr 05 2014