cp's OEIS Frontend

A275550 Number of classes of endofunctions of [n] under reversal and complement to n+1.

%I A275550 #15 Sep 30 2017 23:49:42
%S A275550 1,1,2,10,72,819,11772,206572,4196352,96871525,2500050000,71328400806,
%T A275550 2229026605056,75718793541895,2778001759096256,109473473278652344,
%U A275550 4611686020574871552,206810065502975099529
%N A275550 Number of classes of endofunctions of [n] under reversal and complement to n+1.
%C A275550 Possible classes size are 1,2,4
%C A275550 n 1 2    4
%C A275550 -----------------
%C A275550 1 1 0    0
%C A275550 2 0 2    0
%C A275550 3 1 5    4
%C A275550 4 0 16   56
%C A275550 5 1 74   744
%C A275550 6 0 216  11556
%C A275550 7 1 1371 205200.
%C A275550 Classes of size 2 can be further decomposed by whether the function is stable by reversal or stable by (reversal and complement).
%C A275550 n 2    2-r  2-rc
%C A275550 -----------------
%C A275550 1 0    0    0
%C A275550 2 2    1    1
%C A275550 3 5    4    1
%C A275550 4 16   8    8
%C A275550 5 74   62   12
%C A275550 6 216  108  108
%C A275550 7 1371 1200 171.
%H A275550 Andrew Howroyd, <a href="/A275550/b275550.txt">Table of n, a(n) for n = 0..100</a>
%F A275550 a(n) = (1+(-1)^(n+1)+2*n^n+(3+((-1)^(n+1))*(n-1)+n)*n^(floor(n/2)) )/8.
%F A275550 Classes of size 2: (2 (-1 + (-1)^n) + n^floor(n/2)*(3 + ((-1)^(1 + n))* (-1 + n) + n))/4.
%t A275550 Table[1/8 (1+(-1)^(1+n)+2 n^n+n^Floor[n/2] (3+(-1)^(n+1) (-1+n)+n)),{n,1,17}]
%o A275550 (PARI) a(n) = (1+(-1)^(n+1)+2*n^n+(3+((-1)^(n+1))*(n-1)+n)*n^(floor(n/2)) )/8; \\ _Andrew Howroyd_, Sep 30 2017
%Y A275550 Cf. A000312 All endofunctions
%Y A275550 Cf. A000169 Classes under translation mod n
%Y A275550 Cf. A001700 Classes under sort
%Y A275550 Cf. A056665 Classes under rotation
%Y A275550 Cf. A168658 Classes under complement to n+1
%Y A275550 Cf. A130293 Classes under translation and rotation
%Y A275550 Cf. A081721 Classes under rotation and reversal
%Y A275550 Cf. A275549 Classes under reversal
%Y A275550 Cf. A275550 Classes under reversal and complement
%Y A275550 Cf. A275551 Classes under translation and reversal
%Y A275550 Cf. A275552 Classes under translation and complement
%Y A275550 Cf. A275553 Classes under translation, complement and reversal
%Y A275550 Cf. A275554 Classes under translation, rotation and complement
%Y A275550 Cf. A275555 Classes under translation, rotation and reversal
%Y A275550 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275550 Cf. A275557 Classes under rotation and complement
%Y A275550 Cf. A275558 Classes under rotation, complement and reversal
%Y A275550 Cf. A192396 floor(((k+1)^n-(1+(-1)^k)/2)/2)
%Y A275550 Cf. A275574 (2-r classes)
%K A275550 nonn,easy
%O A275550 0,3
%A A275550 _Olivier Gérard_, Aug 01 2016
%E A275550 Duplicate a(7) removed by _Andrew Howroyd_, Sep 30 2017