A212569 Number of (w,x,y,z) with all terms in {0,...,n} such that range{w,x,y,z} is not one of the numbers w,x,y,z.

0, 1, 2, 31, 96, 321, 690, 1471, 2576, 4465, 6930, 10671, 15312, 21841, 29666, 40111, 52320, 68001, 85986, 108415, 133760, 164641, 199122, 240351, 285936, 339601, 398450, 466831, 541296, 626865, 719490, 824911, 938432, 1066561

Offset: 0

Author

Clark Kimberling, May 29 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Todd Silvestri, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A211795.

Programs

Magma

[((n-1)*n*(2*n*(2*n-5)-3*(-1)^n+11)-2*(-1)^n+2)/4: n in [0..40]]; // Vincenzo Librandi, Nov 16 2014

Mathematica

t = Compile[{{n, Integer}}, Module[{s = 0}, (Do[If[(w != # && x != # && y != # && z != #) &[Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},{x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]]; Map[t[#] &, Range[0, 40]] (* _Peter J. C. Moses, May 24 2012 *)
a[n_Integer/;n>=0]:=((n-1) n (2 n (2 n-5)-3 (-1)^n+11)-2 (-1)^n+2)/4 (* Todd Silvestri, Nov 16 2014 *)
CoefficientList[Series[(- x - 25 x^3 - 36 x^4 - 79 x^5 - 36 x^6 - 15 x^7) / ((-1 + x)^5 (1 + x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 16 2014 *)

PARI

Vec((-x-25*x^3-36*x^4-79*x^5-36*x^6-15*x^7)/(((-1+x)^5)*(1+x)^3)+ O(x^50)) \\ Michel Marcus, Nov 16 2014

Formula

a(n) = n^4 - A212746(n).

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).

G.f.: f(x)/g(x), where f(x)=-x-25*x^3-36*x^4-79*x^5-36*x^6-15*x^7 and g(x)=((-1+x)^5)*(1+x)^3.

a(n) = ((n-1)*n*(2*n*(2*n-5)-3*(-1)^n+11)-2*(-1)^n+2)/4. - Todd Silvestri, Nov 16 2014