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%I #68 Aug 22 2022 15:02:50
%S 0,7,8,15,16,23,24,31,32,39,40,47,48,55,56,63,64,71,72,79,80,87,88,95,
%T 96,103,104,111,112,119,120,127,128,135,136,143,144,151,152,159,160,
%U 167,168,175,176,183,184,191,192,199,200,207,208,215,216,223,224,231,232
%N Numbers that are congruent to {0, 7} mod 8.
%C Numbers such that the n-th triangular number is divisible by 4. - _Charles R Greathouse IV_, Apr 07 2011
%C Except for 0, numbers whose binary reflected Gray code (A014550) ends with 00. - _Amiram Eldar_, May 17 2021
%H David Lovler, <a href="/A047521/b047521.txt">Table of n, a(n) for n = 1..10000</a>
%H Lars Pos, <a href="https://www.pyth.eu/met-kleine-stapjes-grote-sprongen-maken">Met kleine stapjes grote sprongen make</a>, Pythagoras 61-4. Solutions of returning to the origin after steps of increasing width 1,2,3,.. in the 4 directions on a square grid (in Dutch).
%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) - 9 (with a(1)=0). - _Vincenzo Librandi_, Aug 06 2010
%F From _R. J. Mathar_, Oct 08 2011: (Start)
%F a(n) = 3*(-1)^n/2 - 5/2 + 4*n.
%F G.f.: x^2*(7+x) / ( (1+x)*(x-1)^2 ). (End)
%F a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=7 and b(k)=2^(k+2) for k > 0. - _Philippe Deléham_, Oct 17 2011
%F Sum_{n>=2} (-1)^n/a(n) = log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8 - (sqrt(2)+1)*Pi/16. - _Amiram Eldar_, Dec 18 2021
%F E.g.f.: 1 + ((8*x -5)*exp(x) + 3*exp(-x))/2. _David Lovler_, Aug 22 2022
%t {#,#+7}&/@(8*Range[0,30])//Flatten (* or *) LinearRecurrence[{1,1,-1},{0,7,8},60] (* _Harvey P. Dale_, Oct 30 2016 *)
%o (R)
%o kmax <- 10 # by choice
%o a <- c(0,7)
%o for(k in 3:kmax) a <- c(a, a + 2^k)
%o a
%o # _Yosu Yurramendi_, Jan 18 2022
%o (PARI) a(n) = 4*n - 5/2 + 3*(-1)^n/2; \\ _David Lovler_, Jul 25 2022
%Y Union of A008590 and A004771.
%Y Cf. A014550, A030308, A274406.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Aug 06 2010
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