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 A047510 Numbers that are congruent to {2, 4, 6, 7} mod 8. 1
 2, 4, 6, 7, 10, 12, 14, 15, 18, 20, 22, 23, 26, 28, 30, 31, 34, 36, 38, 39, 42, 44, 46, 47, 50, 52, 54, 55, 58, 60, 62, 63, 66, 68, 70, 71, 74, 76, 78, 79, 82, 84, 86, 87, 90, 92, 94, 95, 98, 100, 102, 103, 106, 108, 110, 111, 114, 116, 118, 119, 122, 124 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Wesley Ivan Hurt, May 27 2016: (Start) G.f.: x*(2+2*x+2*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)). a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(n) = (8*n-1-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1). a(2k) = A047535(k), a(2k-1) = A016825(k-1) for k>0. (End) E.g.f.: (2 - cos(x) + 4*x*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - sqrt(2)*log(2*sqrt(2)+3)/16. - Amiram Eldar, Dec 25 2021 MAPLE A047510:=n->(8*n-1-I^(2*n)-I^(-n)-I^n)/4: seq(A047510(n), n=1..100); # Wesley Ivan Hurt, May 27 2016 MATHEMATICA Table[(8n-1-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *) PROG (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016 CROSSREFS Cf. A016825, A047535. Sequence in context: A286047 A325426 A227090 * A189030 A198033 A071260 Adjacent sequences: A047507 A047508 A047509 * A047511 A047512 A047513 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 22 08:23 EDT 2023. Contains 361419 sequences. (Running on oeis4.)