A003143 - OEIS

A003143

a(2*n) = floor( 17*2^n/14 ), a(2*n+1) = floor( 12*2^n/7 ).
(Formerly M0570)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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).

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

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 *)

PROG

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

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

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

CROSSREFS

Cf. A010892, A049347, A077957.

Sequence in context: A343942 A094054 A001521 * A221718 A251571 A017983

Adjacent sequences: A003140 A003141 A003142 * A003144 A003145 A003146

KEYWORD

nonn,easy