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

1,2

Comments

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

Links

Table of n, a(n) for n=1..168.

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).

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)

Example

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

Prog

(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

Crossrefs

Cf. A010887.

Sequence in context: A076819 A355848 A181757 * A082218 A111612 A317920

Adjacent sequences: A181750 A181751 A181752 * A181754 A181755 A181756

Keyword

nonn,easy

Author

Susanna Cuyler, Nov 14 2010

Status

approved