A213395 Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = w.

1, 4, 11, 19, 31, 44, 62, 79, 103, 125, 154, 181, 216, 247, 288, 324, 370, 411, 463, 508, 566, 616, 679, 734, 803, 862, 937, 1001, 1081, 1150, 1236, 1309, 1401, 1479, 1576, 1659, 1762, 1849, 1958, 2050, 2164, 2261, 2381, 2482, 2608, 2714, 2845

Offset

0,2

Comments

For a guide to related sequences, see A212959.

Links

Table of n, a(n) for n=0..46.

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

Formula

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

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

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w == Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]]   (* A213395 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 1, 0, -2, -1, 1, 2, 0]^n*[1; 4; 11; 19; 31; 44; 62])[1, 1] \\ Charles R Greathouse IV, Nov 27 2016

Crossrefs

Cf. A212959.

Sequence in context: A348913 A037262 A101418 * A185873 A009874 A008051

Adjacent sequences: A213392 A213393 A213394 * A213396 A213397 A213398

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2012

Status

approved