A213400 Number of (w,x,y) with all terms in {0,...,n} and w < R < 2*w, where R = range{w,x,y} = max(w,x,y)-min(w,x,y).

0, 0, 0, 2, 6, 19, 29, 52, 81, 116, 159, 223, 282, 366, 462, 568, 688, 841, 987, 1170, 1371, 1586, 1821, 2101, 2372, 2692, 3036, 3398, 3786, 4231, 4665, 5160, 5685, 6232, 6811, 7459, 8094, 8802, 9546, 10316, 11124, 12013, 12887, 13846, 14847

Offset

0,4

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,-1,2,2,0,-1).

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).

G.f.: (2*x^3 + 6*x^4 + 15*x^5 + 13*x^6 + 4*x^7 - x^8 - x^9 )/(1 - 2*x^2 - 2*x^3 + x^4 + 4*x^5 + x^6 - 2*x^7 - 2*x^8 + x^10).

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w < Max[w, x, y] - Min[w, x, y] < 2 w, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A213400 *)

Crossrefs

Cf. A212959.

Sequence in context: A128123 A227884 A186769 * A282080 A273180 A280041

Adjacent sequences: A213397 A213398 A213399 * A213401 A213402 A213403

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2012

Status

approved