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 A047549 Numbers that are congruent to {0, 1, 2, 3, 4, 7} mod 8. 4
 0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 84, 87, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1). FORMULA From Chai Wah Wu, May 29 2016: (Start) a(n) = a(n-1) + a(n-6) - a(n-7) for n>7. G.f.: x^2*(x^5 + 3*x^4 + x^3 + x^2 + x + 1)/(x^7 - x^6 - x + 1). (End) From Wesley Ivan Hurt, Jun 16 2016: (Start) a(n) = (24*n-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+ 2*n)*Pi/6))/18. a(6k) = 8k-1, a(6k-1) = 8k-4, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End) Sum_{n>=2} (-1)^n/a(n) = (14-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8 - (2-sqrt(2))*Pi/16. - Amiram Eldar, Dec 26 2021 MAPLE A047549:=n->(24*n-33+3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)+12*sin((1+ 2*n)*Pi/6))/18: seq(A047549(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016 MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 7, 8}, 50] (* G. C. Greubel, May 29 2016 *) PROG (Magma) [n : n in [0..100] | n mod 8 in [0..4] cat [7]]; // Wesley Ivan Hurt, May 29 2016 CROSSREFS Cf. A047420, A047602. Sequence in context: A351173 A039146 A039106 * A039074 A326966 A326784 Adjacent sequences: A047546 A047547 A047548 * A047550 A047551 A047552 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 10 17:16 EDT 2024. Contains 375058 sequences. (Running on oeis4.)