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 A212501 Number of (w,x,y,z) with all terms in {1,...,n} and w > x < y >= z. 2
 0, 0, 2, 13, 45, 115, 245, 462, 798, 1290, 1980, 2915, 4147, 5733, 7735, 10220, 13260, 16932, 21318, 26505, 32585, 39655, 47817, 57178, 67850, 79950, 93600, 108927, 126063, 145145, 166315, 189720, 215512, 243848, 274890, 308805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For a guide to related sequences, see A211795. Partial sums of A033994. - J. M. Bergot, Jun 14 2013 LINKS Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4. G.f.: x^2*(2+3*x)/(1-x)^5. - Bruno Berselli, May 31 2012 a(n) = (n-1)*n*(n+1)*(5*n-2)/24. - Bruno Berselli, May 31 2012 MAPLE A212501:=n->(n-1)*n*(n+1)*(5*n-2)/24: seq(A212501(n), n=0..60); # Wesley Ivan Hurt, Oct 07 2017 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w > x < y >= z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]]   (* A212501 *) PROG (PARI) a(n)=n*(n-1)*(n+1)*(5*n-2)/24 \\ Charles R Greathouse IV, Jun 14 2013 CROSSREFS Cf. A211795. Sequence in context: A025194 A084156 A002534 * A117717 A176060 A168172 Adjacent sequences:  A212498 A212499 A212500 * A212502 A212503 A212504 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 19 2012 STATUS approved

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Last modified September 30 03:03 EDT 2020. Contains 337432 sequences. (Running on oeis4.)