%I M0570 #52 Nov 06 2022 07:46:52
%S 1,1,2,3,4,6,9,13,19,27,38,54,77,109,155,219,310,438,621,877,1243,
%T 1755,2486,3510,4973,7021,9947,14043,19894,28086,39789,56173,79579,
%U 112347,159158,224694,318317,449389,636635,898779,1273270,1797558
%N a(2*n) = floor( 17*2^n/14 ), a(2*n+1) = floor( 12*2^n/7 ).
%D D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 207.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003143/b003143.txt">Table of n, a(n) for n = 0..1000</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,2,-2).
%F G.f.: (1 +x^3 -x^4 +x^5 -x^6 +x^7)/((1-x)(1-x+x^2)*(1+x+x^2)*(1-2*x^2)). - _Simon Plouffe_
%F a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) + 2*a(n-6) - 2*a(n-7) for n > 7. - _Chai Wah Wu_, May 25 2016
%F a(n) = (1/2)*[n=0] - 2/3 - (1/14)*(2*A010892(n) - 3*A010892(n-1)) + (1/42)*(4*A049347(n) - A049347(n-1)) + (1/14)*(17*A077957(n) + 24*A077957(n-1)). - _G. C. Greubel_, Nov 04 2022
%p A003143:=(1+z**3-z**4+z**5-z**6+z**7)/((z-1)*(z**2-z+1)*(z**2+z+1)*(2*z**2-1)); # [Conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation.]
%t Flatten[Table[{Floor[17 2^n / 14], Floor[12 2^n / 7]}, {n, 0, 30}]] (* _Vincenzo Librandi_, May 27 2016 *)
%o (PARI) a(n)=(17+7*(n%2))*2^(n\2)\14
%o (Magma) [(17+7*(n mod 2))*2^(n div 2) div 14: n in [0..50]]; // _Vincenzo Librandi_, May 27 2016
%o (SageMath) [(((17 +7*(n%2))*2^(n//2))//14) for n in range(51)] # _G. C. Greubel_, Nov 04 2022
%Y Cf. A010892, A049347, A077957.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Michael Somos_, May 04 2000