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 A047482 Numbers that are congruent to {1, 2, 5, 7} mod 8. 2
 1, 2, 5, 7, 9, 10, 13, 15, 17, 18, 21, 23, 25, 26, 29, 31, 33, 34, 37, 39, 41, 42, 45, 47, 49, 50, 53, 55, 57, 58, 61, 63, 65, 66, 69, 71, 73, 74, 77, 79, 81, 82, 85, 87, 89, 90, 93, 95, 97, 98, 101, 103, 105, 106, 109, 111, 113, 114, 117, 119, 121, 122, 125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Colin Barker, May 14 2012: (Start) a(n) = (-5 - (-1)^n + (-i)^n + i^n + 8*n)/4 where i=sqrt(-1). G.f.: x*(1 + x + 3*x^2 + 2*x^3 + x^4)/((1-x)^2*(1+x)*(1+x^2)). (End) a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 17 2012 a(2k) = A047524(k), a(2k-1) = A016813(k-1) for k>0. - Wesley Ivan Hurt, Jun 01 2016 E.g.f.: (2 + cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, Jun 01 2016 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+2)*Pi/16 + log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 24 2021 MAPLE A047482:=n->(-5-(-1)^n+(-I)^n+I^n+8*n)/4: seq(A047482(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016 MATHEMATICA Select[Range[0, 300], MemberQ[{1, 2, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 17 2012 *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 5, 7, 9}, 100] (* G. C. Greubel, Jun 01 2016 *) PROG (Magma) I:=[1, 2, 5, 7, 9]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 17 2012 (PARI) my(x='x+O('x^100)); Vec(x*(1+x+3*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2))) \\ Altug Alkan, Dec 24 2015 CROSSREFS Cf. A016813, A047524. Sequence in context: A186155 A360411 A181713 * A367491 A174272 A062288 Adjacent sequences: A047479 A047480 A047481 * A047483 A047484 A047485 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)