A003143 a(2*n) = floor( 17*2^n/14 ), a(2*n+1) = floor( 12*2^n/7 ).

1, 1, 2, 3, 4, 6, 9, 13, 19, 27, 38, 54, 77, 109, 155, 219, 310, 438, 621, 877, 1243, 1755, 2486, 3510, 4973, 7021, 9947, 14043, 19894, 28086, 39789, 56173, 79579, 112347, 159158, 224694, 318317, 449389, 636635, 898779, 1273270, 1797558

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 207.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,2,-2).

Crossrefs

Cf. A010892, A049347, A077957.

Programs

Magma

[(17+7*(n mod 2))*2^(n div 2) div 14: n in [0..50]]; // Vincenzo Librandi, May 27 2016

Maple

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.]

Mathematica

Flatten[Table[{Floor[17 2^n / 14], Floor[12 2^n / 7]}, {n, 0, 30}]] (* Vincenzo Librandi, May 27 2016 *)

PARI

a(n)=(17+7*(n%2))*2^(n\2)\14

SageMath

[(((17 +7*(n%2))*2^(n//2))//14) for n in range(51)] # G. C. Greubel, Nov 04 2022

Formula

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

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

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

Extensions

More terms from Michael Somos, May 04 2000