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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For a guide to related sequences, see A211795.

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)

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)

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 *)

PROG

(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

CROSSREFS

Cf. A211795.

Sequence in context: A307091 A024847 A154516 * A298174 A249743 A298140

Adjacent sequences:  A212741 A212742 A212743 * A212745 A212746 A212747

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 26 2012

STATUS

approved

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Last modified February 26 17:22 EST 2021. Contains 341632 sequences. (Running on oeis4.)