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

0,3

Comments

For a guide to related sequences, see A211795.

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A211795.

Sequence in context: A282725 A030459 A141978 * A101254 A243472 A336788

Adjacent sequences: A212566 A212567 A212568 * A212570 A212571 A212572

Keyword

nonn,easy

Author

Clark Kimberling, May 29 2012

Status

approved