A212744 Number of (w,x,y,z) with all terms in {0,...,n} and w=max{w,x,y,z}-min{w,x,y,z}; i.e., the range of (w,x,y,z) is its first term.
1, 8, 34, 83, 181, 314, 532, 791, 1177, 1604, 2206, 2843, 3709, 4598, 5776, 6959, 8497, 10016, 11962, 13859, 16261, 18578, 21484, 24263, 27721, 31004, 35062, 38891, 43597, 48014, 53416, 58463, 64609, 70328, 77266, 83699, 91477, 98666, 107332, 115319, 124921
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1)
Crossrefs
Cf. A211795.
Programs
-
Mathematica
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w == Max[w, x, y, z] - Min[w, x, y, z], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]]; Map[t[#] &, Range[0, 40]] (* A212744 *) -
PARI
Vec((1+x+x^2)*(x^4+6*x^3+16*x^2+6*x+1)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 28 2016
Formula
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).
G.f.: (1+x+x^2)*(x^4+6*x^3+16*x^2+6*x+1) / ((1+x)^3*(x-1)^4).
From Colin Barker, Jan 28 2016: (Start)
a(n) = (30*n^3+3*((-1)^n+15)*n^2+3*((-1)^n+15)*n+(-1)^n+15)/16.
a(n) = (15*n^3+24*n^2+24*n+8)/8 for n even.
a(n) = (15*n^3+21*n^2+21*n+7)/8 for n odd.
(End)
Comments