This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A062867 Triangle read by rows: entries give numbers of permutations of [1..n] by absolute barycenter. 5
 1, 1, 2, 4, 2, 14, 8, 2, 46, 62, 10, 2, 282, 292, 132, 12, 2, 1394, 2578, 784, 268, 14, 2, 12658, 15472, 9718, 1920, 534, 16, 2, 83122, 171662, 69318, 33230, 4470, 1058, 18, 2, 985730, 1282604, 964544, 276044, 107660, 10100, 2096, 20, 2, 8012962, 17465978, 8199268, 4851200, 1022824, 337988, 22396, 4160, 22, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The barycenter or signcenter of a permutation is the sum of the signs of the difference between initial and final positions of the objects. LINKS Alois P. Heinz, Rows n = 0..20, flattened FORMULA T(n,0) = A062868(n) = A062866(n,0), T(n,k) = 2 * A062866(n,k) for k>0. - Alois P. Heinz, Jul 31 2018 EXAMPLE [1], [2], [4, 2], [14, 8, 2], [46, 62, 10, 2], [282, 292, 132, 12, 2], ... (1,6,2,3,4,5,7) has difference (0,5,-1,-1,-1,-1,0) and signs (0,1,-1,-1,-1,-1,0) with total -3, absolute value is 3. This is one of 268 such permutations of degree 7. Triangle T(n,k) begins:        1;        1;        2;        4,       2;       14,       8,      2;       46,      62,     10,      2;      282,     292,    132,     12,      2;     1394,    2578,    784,    268,     14,     2;    12658,   15472,   9718,   1920,    534,    16,    2;    83122,  171662,  69318,  33230,   4470,  1058,   18,  2;   985730, 1282604, 964544, 276044, 107660, 10100, 2096, 20, 2; MAPLE b:= proc(s, t) option remember; (n-> `if`(n=0, x^t,       add(b(s minus {j}, t+signum(n-j)), j=s)))(nops(s))     end: T:= n-> (p-> seq(coeff(p, x, i)*`if`(i=0, 1, 2), i=0..degree(p)))(b({\$1..n}, 0)): seq(T(n), n=0..12);  # Alois P. Heinz, Jul 31 2018 CROSSREFS Column k=0 gives A062868. Cf. A062866. Sequence in context: A006018 A152666 A153801 * A264027 A113539 A215055 Adjacent sequences:  A062864 A062865 A062866 * A062868 A062869 A062870 KEYWORD nice,nonn,tabf AUTHOR Olivier Gérard, Jun 26 2001 EXTENSIONS More terms from Vladeta Jovovic, Jun 29 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 21:45 EST 2019. Contains 329809 sequences. (Running on oeis4.)