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A146512
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Numbers congruent to {1, 3} mod 12.
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5
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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
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OFFSET
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1,2
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COMMENTS
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Positive integers k such that Hypergeometric[k/4,(4-k)/4,1/2,3/4] = 2Cos[Pi/6]
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LINKS
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Table of n, a(n) for n=1..56.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
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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
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EXAMPLE
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G.f. = x + 3*x^2 + 13*x^3 + 15*x^4 + 25*x^5 + 27*x^6 + 37*x^7 + 39*x^8 + ...
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MATHEMATICA
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Select[Range[300], MemberQ[{1, 3}, Mod[#, 12]]&] (* Ray Chandler, Dec 06 2016 *)
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PROG
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(PARI) {a(n) = 6*n - 9 + n%2*4}; /* Michael Somos, Dec 06 2016 */
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CROSSREFS
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Cf. A146507, A146509, A146510, A146511.
Sequence in context: A045233 A113487 A032623 * A082704 A353060 A152270
Adjacent sequences: A146509 A146510 A146511 * A146513 A146514 A146515
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KEYWORD
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nonn,easy
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AUTHOR
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Artur Jasinski, Oct 30 2008
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EXTENSIONS
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Formula and crossrefs corrected by Ray Chandler, Dec 06 2016
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STATUS
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approved
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