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%I #35 Sep 03 2022 08:50:26
%S 1,2,9,10,17,18,25,26,33,34,41,42,49,50,57,58,65,66,73,74,81,82,89,90,
%T 97,98,105,106,113,114,121,122,129,130,137,138,145,146,153,154,161,
%U 162,169,170,177,178,185,186,193,194,201,202,209,210,217,218,225,226,233
%N Numbers that are congruent to {1, 2} mod 8.
%H David Lovler, <a href="/A047468/b047468.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 8*n - a(n-1) - 13 (with a(1)=1). - _Vincenzo Librandi_, Aug 06 2010
%F G.f.: x*(1+x+6*x^2)/((1-x)^2*(1+x)). - _Colin Barker_, May 13 2012
%F a(n) = 1 + 8*floor((n-1)/2) + ((n-1) mod 2). - _Alois P. Heinz_, May 13 2012
%F a(n) = (-3*(3 + (-1)^n) + 8*n)/2. - _Colin Barker_, May 14 2012
%F a(1)=1, a(2)=2, a(3)=9, a(n) = a(n-1) + a(n-2) - a(n-3). - _Harvey P. Dale_, Mar 26 2013
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 18 2021
%F E.g.f.: 6 + ((8*x - 9)*exp(x) - 3*exp(-x))/2. - _David Lovler_, Sep 02 2022
%t Flatten[#+{1,2}&/@(8Range[0,30])] (* or *) LinearRecurrence[{1,1,-1},{1,2,9},60] (* _Harvey P. Dale_, Mar 26 2013 *)
%o (PARI) a(n)=(n-1)\2*8+2-n%2 \\ _Charles R Greathouse IV_, May 14 2012
%Y Union of A017077 and A017089.
%Y Cf. A047467.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Aug 06 2010
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