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 A287818 Number of nonary sequences of length n such that no two consecutive terms have distance 3. 0
 1, 9, 69, 531, 4089, 31491, 242529, 1867851, 14385369, 110789811, 853254609, 6571393371, 50609994249, 389776014531, 3001884188289, 23119197549291, 178053936060729, 1371293449053651, 10561101680875569, 81336980637343611, 626421808927336809, 4824426473972595171 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. Index entries for linear recurrences with constant coefficients, signature (9, -10). FORMULA For n>2, a(n) = 9*a(n-1) - 10*a(n-2), a(0)=1, a(1)=9, a(2)=69. G.f.: (1 - 2 x^2)/(1 - 9 x + 10 x^2). For n>0, a(n)=(1/5)(3 - 18/sqrt(41))*((9 - sqrt(41))/2)^n + (1/5)(3 + 18/sqrt(41))*((9 + sqrt(41))/2)^n. a(n) = A178869(n+1)-2*A178869(n-1). - R. J. Mathar, Oct 20 2019 EXAMPLE For n=2 the a(2) = 81 - 12 = 69 sequences contain every combination except these twelve: 03,30,14,41,25,52,36,63,47,74,58,85. MATHEMATICA LinearRecurrence[{9, -10}, {1, 9, 69}, 40] PROG (Python) def a(n): .if n in [0, 1, 2]: ..return [1, 9, 69][n] .return 9*a(n-1)-10*a(n-2) CROSSREFS Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. Sequence in context: A361139 A081616 A299915 * A297222 A126530 A351810 Adjacent sequences: A287815 A287816 A287817 * A287819 A287820 A287821 KEYWORD nonn,easy AUTHOR David Nacin, Jun 02 2017 STATUS approved

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Last modified October 1 12:35 EDT 2023. Contains 365826 sequences. (Running on oeis4.)