%I A101986
%S A101986 0,2,9,23,46,80,127,189,268,366,485,627,794,988,1211,1465,1752,2074,
%T A101986 2433,2831,3270,3752,4279,4853,5476,6150,6877,7659,8498,9396,10355,
%U A101986 11377,12464,13618,14841,16135,17502,18944,20463,22061,23740,25502
%N A101986 a(n) is the maximum sum of products of successive pairs in a permutation 
               of order n.
%C A101986 1 3 5 4 2 is the 11th permutation, in lexical order. of order 5. Its 
               reverse 2 4 5 3 1 is the 41st. The earliest permutation of order 
               6 is the 41st, 1 3 5 6 4 2. This pattern continues as far as I have 
               looked, so its reversal 2 4 6 5 3 1 is the 191st and the earliest 
               permutation of order 7 is the 191st, et cetera.
%C A101986 Comments from Dmitry Kamenetsky (Dmitry.Kamenetsky(AT)rsise.anu.edu.au), 
               Dec 15 2006: (Start) "This sequence is related to A026035, except 
               here we take the maximum sum of products of successive pairs. Here 
               is a method for generating such permutations. Start with two lists, 
               the first has numbers 1 to n, while the second is empty.
%C A101986 "Repeat the following operations until the first list is empty: 1. Move 
               the smallest number of the first list to the leftmost available position 
               in the second list. The move operation removes the original number 
               from the first list. 2. Move the smallest number of the first list 
               to the rightmost available position in the second list. For example 
               when n=8, the permutation is 1, 3, 5, 7, 8, 6, 4, 2." (End)
%C A101986 a(n+1) = a(n) + A008865(n+2); a(n) = A160805(n) - 4. [From Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), May 26 2009]
%D A101986 Message from Leroy Quet on January 28, 2005 6:45:43 PM PST to the sequence 
               list, asking for someone to provide more values and to submit these 
               to OEIS.
%H A101986 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A101986 a(n) = (n+9n^2+2n^3)/6.
%e A101986 The permutations of order 5 with maximum sum of products is 1 3 5 4 2 
               and its reverse, since (1*3)+(3*5)+(5*4)+(4*2) is 46. All others 
               are empirically less than 46.
%p A101986 a:=n->sum((n+j^2),j=1..n): seq(a(n),n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 27 2006
%t A101986 Table[(n + 9n^2 + 2n^3)/6, {n, 0, 41}] (from Robert G. Wilson v Feb 04 
               2005)
%o A101986 (J language): the polynomial P such that P(n) is a(n) is: 0 1 9 2 & p. 
               % 6 & p. (A)
%o A101986 where 0 1 9 2 are the coefficients in ascending order of the numerator 
               of a rational polynomial and 6 is the (constant) coefficient of its 
               denominator. J's primitive function p. produces a polynomial with 
               these coefficients. Division is indicated by % . Thus the J expression 
               (A) is equivalent to the formula above.
%Y A101986 Pairwise sums of A005581.
%Y A101986 Cf. A026035.
%Y A101986 Sequence in context: A027702 A051897 A032636 this_sequence A023542 A023654 
               A062445
%Y A101986 Adjacent sequences: A101983 A101984 A101985 this_sequence A101987 A101988 
               A101989
%K A101986 easy,nonn
%O A101986 0,2
%A A101986 Eugene McDonnell (eemcd(AT)mac.com), Jan 29 2005