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 A213483 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| >= w+x+y. 3
 1, 5, 13, 23, 38, 55, 78, 103, 135, 169, 211, 255, 308, 363, 428, 495, 573, 653, 745, 839, 946, 1055, 1178, 1303, 1443, 1585, 1743, 1903, 2080, 2259, 2456, 2655, 2873, 3093, 3333, 3575, 3838, 4103, 4390, 4679, 4991, 5305, 5643, 5983, 6348 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) + A213482(n) = (n+1)^3. For a guide to related sequences, see A212959. LINKS Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6). G.f.: (1 + 3*x + 2*x^2 - 4*x^3 - 2*x^4 + x^5)/((1 - x)^4 (1 + x)^2)). From Ayoub Saber Rguez, Dec 31 2021: (Start) a(n) + A213482(n) = (n+1)^3. a(n) = A213479(n) + A006918(n). a(n)= (n^3 + 33*n^2 + 71*n + 15 + (3*n+9)*((n+1) mod 2))/24. (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x + y <= Abs[w - x] + Abs[x - y], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]]; Map[t[#] &, Range[0, 60]]   (* A213483 *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 5, 13, 23, 38, 55}, 50] (* Harvey P. Dale, Sep 11 2019 *) CROSSREFS Cf. A212959. Sequence in context: A074798 A031336 A099958 * A049833 A083800 A075829 Adjacent sequences:  A213480 A213481 A213482 * A213484 A213485 A213486 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 13 2012 STATUS approved

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Last modified July 4 08:01 EDT 2022. Contains 355070 sequences. (Running on oeis4.)