cp's OEIS Frontend

A087035 Maximum value taken on by f(P) = Sum_{i=1..n} p(i)*p(n+1-i) as {p(1),p(2),...,p(n)} ranges over all permutations P of {1,2,3,...,n}.

%I A087035 #30 Aug 24 2024 20:16:20
%S A087035 0,1,4,13,28,53,88,137,200,281,380,501,644,813,1008,1233,1488,1777,
%T A087035 2100,2461,2860,3301,3784,4313,4888,5513,6188,6917,7700,8541,9440,
%U A087035 10401,11424,12513,13668,14893,16188,17557,19000,20521,22120,23801,25564,27413,29348
%N A087035 Maximum value taken on by f(P) = Sum_{i=1..n} p(i)*p(n+1-i) as {p(1),p(2),...,p(n)} ranges over all permutations P of {1,2,3,...,n}.
%C A087035 The corresponding minimum value of f(P) is given by A000292(n)=binomial(n+3,3).
%C A087035 The number of distinct values of f(P) is given by A087034.
%C A087035 Also, number of (w,x,y) with all terms in {0,...,n-1} and 2|w-x| <= max(w,x,y)-min(w,x,y). For a guide to related sequences, see A212959. - _Clark Kimberling_, Jun 10 2012
%H A087035 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A087035 From _Clark Kimberling_, Jun 10 2012: (Start)
%F A087035 a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F A087035 G.f.: (x + x^2 + 3*x^3 - x^4)/(((1 - x)^4)*(1 + x)).
%F A087035 a(n+1) + A213045(n) = (n+1)^3. (End)
%F A087035 a(n) = (2*(n-1)*(n+1)*(2*n+3)-3*(-1)^n+9)/12. - _Bruno Berselli_, Jun 11 2012
%e A087035 a(3)=13, since f takes on the values 10 and 13: f({1,2,3})=10, f({1,3,2})=13, f({2,1,3})=13, f({2,3,1})=13, f({3,1,2})=13 and f({3,2,1})=10.
%t A087035 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A087035 (Do[If[Max[w, x, y] - Min[w, x, y] >= 2 Abs[w - x],
%t A087035   s = s + 1],
%t A087035 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A087035 m = Map[t[#] &, Range[0, 45]]
%Y A087035 Cf. A000292, A087034, A110610, A212959.
%K A087035 nonn,easy
%O A087035 0,3
%A A087035 _John W. Layman_, Jul 31 2003
%E A087035 a(11) and a(12) from _R. J. Mathar_, Jun 26 2012
%E A087035 Merged with a sequence of Clark Kimberling by _Max Alekseyev_, Jun 27 2012
%E A087035 a(0)=0 prepended by _Alois P. Heinz_, Aug 24 2024