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 A287829 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 6. 0
 1, 10, 92, 848, 7816, 72040, 663992, 6120008, 56408056, 519912520, 4792028792, 44168084168, 407096815096, 3752207504200, 34584061167992, 318760965520328, 2938016812018936, 27079673239211080, 249593092776937592, 2300497181470860488, 21203660818791619576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, the number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 5+k for k in {0,1,2,3,4} is given by a(n) = 9*a(n-1) + 2*k*a(n-2), a(0)=1, a(1)=10. LINKS Index entries for linear recurrences with constant coefficients, signature (9, 2). FORMULA a(n) = 9*a(n-1) + 2*a(n-2), a(0)=1, a(1)=10. G.f.: (-1 - x)/(-1 + 9*x + 2*x^2). a(n) = ((1 - 11/sqrt(89))/2)*((9 - sqrt(89))/2)^n + ((1 + 11/sqrt(89))/2)*((9 + sqrt(89))/2)^n. a(n) = A015579(n)+A015579(n+1). - R. J. Mathar, Oct 20 2019 MATHEMATICA LinearRecurrence[{9, 2}, {1, 10}, 30] PROG (Python) def a(n): .if n in [0, 1]: ..return [1, 10][n] .return 9*a(n-1)+2*a(n-2) CROSSREFS Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831. Sequence in context: A037534 A120996 A190990 * A265242 A262173 A103944 Adjacent sequences:  A287826 A287827 A287828 * A287830 A287831 A287832 KEYWORD nonn,easy AUTHOR David Nacin, Jun 02 2017 STATUS approved

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Last modified January 22 13:21 EST 2021. Contains 340362 sequences. (Running on oeis4.)