A181753 Universal sequence of period 56 which contains every 3-subset of {1,2,...,8} exactly once.

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, 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, 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

Offset: 1

Author

Susanna Cuyler, Nov 14 2010

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

• G. Hurlbert, On universal cycles for k-subsets of an n-element set, SIAM J. Discrete Math., 7 (1994), 598-604.
• A. Leitner and A. Godbole, Universal cycles of classes of restricted words, Discrete Math., 310 (2010) 3303-3309.
• Index entries for linear recurrences with constant coefficients, 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).

Crossrefs

Cf. A010887.

Programs

Haskell

a181753 n = a181753_list !! (n-1)
a181753_list = concat $ iterate
               (map ((+ 1) . flip mod 8 . (+ 4))) [1,3,5,6,7,2,5]
-- Reinhard Zumkeller, Nov 09 2014

Formula

From Chai Wah Wu, Jun 13 2020: (Start)

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.

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)