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A253195 Numbers congruent to 5 or 8 mod 9.

%I A253195 #22 Sep 07 2022 10:25:12
%S A253195 5,8,14,17,23,26,32,35,41,44,50,53,59,62,68,71,77,80,86,89,95,98,104,
%T A253195 107,113,116,122,125,131,134,140,143,149,152,158,161,167,170,176,179,
%U A253195 185,188,194,197,203,206,212,215,221,224,230,233,239,242,248,251
%N A253195 Numbers congruent to 5 or 8 mod 9.
%C A253195 These numbers cannot be written as the sum of two triangular numbers.
%H A253195 Arkadiusz Wesolowski, <a href="/A253195/b253195.txt">Table of n, a(n) for n = 1..1000</a>
%H A253195 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A253195 a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.
%F A253195 G.f.: x*(5 + 3*x + x^2)/((1 + x)*(1 - x)^2).
%F A253195 a(n) = a(n-2) + 9.
%F A253195 a(n) = 9*n - a(n-1) - 5.
%F A253195 a(n) = 4*n + 2*ceiling(n/2) - floor(n/2) - 1.
%F A253195 a(n) = (9*n - (3/2)*(1 + (- 1)^n) + 1)/2.
%F A253195 E.g.f.: 1 + ((18*x - 1)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Sep 06 2022
%t A253195 LinearRecurrence[{1, 1, -1}, {5, 8, 14}, 56]
%t A253195 Select[Range[300],MemberQ[{5,8},Mod[#,9]]&] (* _Harvey P. Dale_, Mar 17 2020 *)
%o A253195 (Magma) [n: n in [0..251] | n mod 9 in {5, 8}];
%o A253195 (PARI) Vec(x*(5 + 3*x + x^2)/((1 + x)*(1 - x)^2) + O(x^80)) \\ _Michel Marcus_, Mar 25 2015
%Y A253195 Subsequence of A014132 and of A020757.
%K A253195 nonn,easy
%O A253195 1,1
%A A253195 _Arkadiusz Wesolowski_, Mar 24 2015