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 A275550 Number of classes of endofunctions of [n] under reversal and complement to n+1. 14
 1, 1, 2, 10, 72, 819, 11772, 206572, 4196352, 96871525, 2500050000, 71328400806, 2229026605056, 75718793541895, 2778001759096256, 109473473278652344, 4611686020574871552, 206810065502975099529 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Possible classes size are 1,2,4 n 1 2    4 ----------------- 1 1 0    0 2 0 2    0 3 1 5    4 4 0 16   56 5 1 74   744 6 0 216  11556 7 1 1371 205200. Classes of size 2 can be further decomposed by whether the function is stable by reversal or stable by (reversal and complement). n 2    2-r  2-rc ----------------- 1 0    0    0 2 2    1    1 3 5    4    1 4 16   8    8 5 74   62   12 6 216  108  108 7 1371 1200 171. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 FORMULA a(n) = (1+(-1)^(n+1)+2*n^n+(3+((-1)^(n+1))*(n-1)+n)*n^(floor(n/2)) )/8. Classes of size 2: (2 (-1 + (-1)^n) + n^floor(n/2)*(3 + ((-1)^(1 + n))* (-1 + n) + n))/4. MATHEMATICA Table[1/8 (1+(-1)^(1+n)+2 n^n+n^Floor[n/2] (3+(-1)^(n+1) (-1+n)+n)), {n, 1, 17}] PROG (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 CROSSREFS Cf. A000312 All endofunctions Cf. A000169 Classes under translation mod n Cf. A001700 Classes under sort Cf. A056665 Classes under rotation Cf. A168658 Classes under complement to n+1 Cf. A130293 Classes under translation and rotation Cf. A081721 Classes under rotation and reversal Cf. A275549 Classes under reversal Cf. A275550 Classes under reversal and complement Cf. A275551 Classes under translation and reversal Cf. A275552 Classes under translation and complement Cf. A275553 Classes under translation, complement and reversal Cf. A275554 Classes under translation, rotation and complement Cf. A275555 Classes under translation, rotation and reversal Cf. A275556 Classes under translation, rotation, complement and reversal Cf. A275557 Classes under rotation and complement Cf. A275558 Classes under rotation, complement and reversal Cf. A192396 floor(((k+1)^n-(1+(-1)^k)/2)/2) Cf. A275574 (2-r classes) Sequence in context: A277502 A231039 A224799 * A243250 A088189 A228609 Adjacent sequences:  A275547 A275548 A275549 * A275551 A275552 A275553 KEYWORD nonn,easy AUTHOR Olivier Gérard, Aug 01 2016 EXTENSIONS Duplicate a(7) removed by Andrew Howroyd, Sep 30 2017 STATUS approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)