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%I #48 Sep 08 2022 08:46:22
%S 1,7,9,11,17,19,21,27,29,31,37,39,41,47,49,51,57,59,61,67,69,71,77,79,
%T 81,87,89,91,97,99,101,107,109,111,117,119,121,127,129,131,137,139,
%U 141,147,149,151,157,159,161,167,169
%N Numbers congruent to {1, 7, 9} mod 10.
%C When multiplied by 10, one gets the numbers ending in "dix" in French (10, 70, 90, 110, ...).
%H G. C. Greubel, <a href="/A317633/b317633.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n) = a(n-3) + 10, a(1) = 1, a(2) = 7, a(3) = 9.
%F From _Bruno Berselli_, Jul 02 2018: (Start)
%F G.f.: x*(1 + 6*x + 2*x^2 + x^3)/((1 - x)^2*(1 + x + x^2)).
%F a(n) = 2*n + 4*floor((n+1)/3) - 1. (End)
%e G.f. = x + 7*x^2 + 9*x^3+ 11*x^4 + 17*x^5 + 19*x^6 + 21*x^7 + 27*x^8 + ... - _Michael Somos_, Aug 19 2018
%t Table[2 n + 4 Floor[(n + 1)/3] - 1, {n, 1, 60}] (* _Bruno Berselli_, Jul 02 2018 *)
%t Select[Range[0, 250], MemberQ[{1, 7, 9}, Mod[#, 10]]&] (* _Vincenzo Librandi_, Aug 05 2018 *)
%t CoefficientList[ Series[(x^3 + 2x^2 + 6x + 1)/((x - 1)^2 (x^2 + x + 1)), {x, 0, 60}], x] (* or *)
%t LinearRecurrence[{1, 0, 1, -1}, {1, 7, 9, 11}, 61] (* _Robert G. Wilson v_, Aug 08 2018 *)
%o (Magma) [n: n in [0..170]|n mod 10 in {1, 7, 9}]; // _Vincenzo Librandi_, Aug 05 2018
%o (PARI) x='x+O('x^60); Vec(x*(1+6*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2))) \\ _G. C. Greubel_, Aug 08 2018
%Y Cf. A008592, A010692.
%K nonn,easy
%O 1,2
%A _Paul Curtz_, Aug 02 2018
%E Definition from _Jianing Song_, Aug 02 2018
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