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 A146512 Numbers congruent to {1, 3} mod 12. 5
 1, 3, 13, 15, 25, 27, 37, 39, 49, 51, 61, 63, 73, 75, 85, 87, 97, 99, 109, 111, 121, 123, 133, 135, 145, 147, 157, 159, 169, 171, 181, 183, 193, 195, 205, 207, 217, 219, 229, 231, 241, 243, 253, 255, 265, 267, 277, 279, 289, 291, 301, 303, 313, 315, 325, 327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Positive integers k such that Hypergeometric[k/4,(4-k)/4,1/2,3/4] = 2Cos[Pi/6] LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(2k-1) = 12*(k-1)+1, a(2k) = 12*(k-1)+3, where k>0. a(n) = 8*floor(n/2) + 2*n +1, with offset 0..a(0)= 1 a(n) = 6*n -1 + 2*(-1)^n, with offset 0..a(0)=1. [Gary Detlefs, Mar 13 2010] a(n) = 12*n-a(n-1)-20 (with a(1)=1). [Vincenzo Librandi, Nov 26 2010] G.f.: x * (1 + 2*x + 9*x^2) / (1 - x - x^2 + x^3). - Michael Somos, Dec 06 2016 a(n) = a(n-1)+a(n-2)-a(n-3). - Wesley Ivan Hurt, May 03 2021 EXAMPLE G.f. = x + 3*x^2 + 13*x^3 + 15*x^4 + 25*x^5 + 27*x^6 + 37*x^7 + 39*x^8 + ... MATHEMATICA Select[Range[300], MemberQ[{1, 3}, Mod[#, 12]]&] (* Ray Chandler, Dec 06 2016 *) PROG (PARI) {a(n) = 6*n - 9 + n%2*4}; /* Michael Somos, Dec 06 2016 */ CROSSREFS Cf. A146507, A146509, A146510, A146511. Sequence in context: A045233 A113487 A032623 * A082704 A353060 A152270 Adjacent sequences:  A146509 A146510 A146511 * A146513 A146514 A146515 KEYWORD nonn,easy AUTHOR Artur Jasinski, Oct 30 2008 EXTENSIONS Formula and crossrefs corrected by Ray Chandler, Dec 06 2016 STATUS approved

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Last modified May 26 02:45 EDT 2022. Contains 354074 sequences. (Running on oeis4.)