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 A212257 Number of (v,w,x,y,z) with all terms in {0,1,...,n} and v=average(w,x,y,z). 2
 1, 2, 21, 64, 157, 322, 601, 1024, 1641, 2498, 3661, 5184, 7141, 9602, 12657, 16384, 20881, 26242, 32581, 40000, 48621, 58562, 69961, 82944, 97657, 114242, 132861, 153664, 176821, 202498, 230881, 262144, 296481, 334082, 375157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For a guide to related sequences, see A211795. LINKS Index entries for linear recurrences with constant coefficients, signature (4,-6,4,0,-4,6,-4,1) FORMULA a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-4*a(n-5)+6*a(n-6)-4*a(n-7)+a(n-8). From Benedict W. J. Irwin, Sep 05 2016: (Start) a(n) = (1+7*(-1)^n)/8+n+3*n^2/2+n^3+n^4/4-sin(n*Pi/2). G.f.: 7/(8*(1+x))-x/(1+x^2)+(-1-26*x-16*x^2-6*x^3+x^4)/(8*(x-1)^5). (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[4 v == w + x + y + z, s = s + 1], {v, 0, #}, {w, 0, #}, {x, 0, #}, {y, 0, #}, {z, 0, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]]   (* A212257 *) (* Peter J. C. Moses, Apr 13 2012 *) Table[(1+7(-1)^n)/8+n+3n^2/2+n^3+n^4/4-Sin[n Pi/2], {n, 0, 30}] (* Benedict W. J. Irwin, Sep 05 2016 *) CROSSREFS Cf. A211795. Sequence in context: A097718 A180232 A075681 * A034520 A111128 A213827 Adjacent sequences:  A212254 A212255 A212256 * A212258 A212259 A212260 KEYWORD nonn AUTHOR Clark Kimberling, May 15 2012 STATUS approved

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)