A181753 - OEIS

%I #30 Dec 08 2021 12:06:26

%S 1,3,5,6,7,2,5,6,8,2,3,4,7,2,3,5,7,8,1,4,7,8,2,4,5,6,1,4,5,7,1,2,3,6,

%T 1,2,4,6,7,8,3,6,7,1,3,4,5,8,3,4,6,8,1,2,5,8,1,3,5,6,7,2,5,6,8,2,3,4,

%U 7,2,3,5,7,8,1,4,7,8,2,4,5,6,1,4,5,7,1,2,3,6,1,2,4,6,7,8,3,6,7,1,3,4,5,8,3,4,6,8,1,2,5,8,1,3,5,6,7,2,5,6,8,2,3,4,7,2,3,5,7,8,1,4,7,8,2,4,5,6,1,4,5,7,1,2,3,6,1,2,4,6,7,8,3,6,7,1,3,4,5,8,3,4,6,8,1,2,5,8

%N Universal sequence of period 56 which contains every 3-subset of {1,2,...,8} exactly once.

%C Each successive block of length 7 is obtained by adding 5 mod 8 to the previous block.

%H G. Hurlbert, <a href="https://doi.org/10.1137/S0895480191220861">On universal cycles for k-subsets of an n-element set</a>, SIAM J. Discrete Math., 7 (1994), 598-604.

%H A. Leitner and A. Godbole, <a href="https://doi.org/10.1016/j.disc.2010.07.016">Universal cycles of classes of restricted words</a>, Discrete Math., 310 (2010) 3303-3309.

%H <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1,0,0,0,0,0,-1, 1).

%F From _Chai Wah Wu_, Jun 13 2020: (Start)

%F a(n) = a(n-1) - a(n-7) + a(n-8) - a(n-14) + a(n-15) - a(n-21) + a(n-22) - a(n-28) + a(n-29) - a(n-35) + a(n-36) - a(n-42) + a(n-43) - a(n-49) + a(n-50) for n > 50.

%F G.f.: x*(-8*x^49 + 3*x^48 + 3*x^47 + x^46 - 7*x^45 + 2*x^44 + 2*x^43 - 7*x^42 - 2*x^41 + 6*x^40 + 2*x^39 - 6*x^38 + 4*x^37 - 4*x^36 - 6*x^35 + x^34 + x^33 + 3*x^32 - 5*x^31 + 6*x^30 - 2*x^29 - 5*x^28 - 4*x^27 + 4*x^26 + 4*x^25 - 4*x^24 - 4*x^21 - x^20 - x^19 + 5*x^18 - 3*x^17 + 2*x^16 - 6*x^15 - 3*x^14 + 2*x^13 + 2*x^12 - 2*x^11 - 2*x^10 + 4*x^9 - 4*x^8 - 2*x^7 - 3*x^6 + 5*x^5 - x^4 - x^3 - 2*x^2 - 2*x - 1)/(x^50 - x^49 + x^43 - x^42 + x^36 - x^35 + x^29 - x^28 + x^22 - x^21 + x^15 - x^14 + x^8 - x^7 + x - 1). (End)

%e The period is 1356725 6823472 3578147 8245614 5712361 2467836 7134583 4681258.

%o (Haskell)

%o a181753 n = a181753_list !! (n-1)

%o a181753_list = concat $ iterate

%o                (map ((+ 1) . flip mod 8 . (+ 4))) [1,3,5,6,7,2,5]

%o -- _Reinhard Zumkeller_, Nov 09 2014

%Y Cf. A010887.

%K nonn,easy

%O 1,2

%A _Susanna Cuyler_, Nov 14 2010