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 A212748 Number of (w,x,y,z) with all terms in {0,...,n} and w=2*floor((x+y+z)/2)). 1
 1, 4, 17, 20, 53, 56, 117, 120, 217, 220, 361, 364, 557, 560, 813, 816, 1137, 1140, 1537, 1540, 2021, 2024, 2597, 2600, 3273, 3276, 4057, 4060, 4957, 4960, 5981, 5984, 7137, 7140, 8433, 8436, 9877, 9880, 11477, 11480, 13241, 13244, 15177 (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+3*x+10*x^2-6*x^3-3*x^4+3*x^5) / ((1+x)^3*(x-1)^4). From Colin Barker, Jan 29 2016: (Start) a(n) = (2*n^3+3*((-1)^n+5)*n^2+(15*(-1)^n+37)*n+12)/12. a(n) = (n^3+9*n^2+26*n+6)/6 for n even. a(n) = (n^3+6*n^2+11*n+6)/6 for n odd. (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w == 2*Floor[(x + y + z)/2], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]]; Map[t[#] &, Range[0, 45]]   (* A212748 *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 4, 17, 20, 53, 56, 117}, 50] (* Harvey P. Dale, Jun 08 2018 *) PROG (PARI) Vec((1+3*x+10*x^2-6*x^3-3*x^4+3*x^5)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 29 2016 CROSSREFS Cf. A211795. Sequence in context: A031444 A031033 A128981 * A032828 A193379 A022134 Adjacent sequences:  A212745 A212746 A212747 * A212749 A212750 A212751 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 28 2012 STATUS approved

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Last modified April 23 13:56 EDT 2021. Contains 343204 sequences. (Running on oeis4.)