A001640 A Fielder sequence. (Formerly M3358 N1352)

1, 1, 4, 9, 16, 28, 43, 73, 130, 226, 386, 660, 1132, 1947, 3349, 5753, 9878, 16966, 29147, 50074, 86020, 147764, 253829, 436036, 749041, 1286728, 2210377, 3797047, 6522681, 11204863, 19248056, 33064889, 56799857, 97572504, 167612993, 287930658, 494615964

Offset

1,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70.

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, 0, 1, 1, 1, 1).

Formula

G.f.: x*(1+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6).

Maple

A001640:=-(1+3*z**2+4*z**3+5*z**4+6*z**5)/(-1+z+z**3+z**4+z**5+z**6); # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

LinearRecurrence[{1, 0, 1, 1, 1, 1}, {1, 1, 4, 9, 16, 28}, 50] (* T. D. Noe, Aug 09 2012 *)

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6)+x*O(x^n), n))
(Magma) I:=[1, 1, 4, 9, 16, 28]; [n le 6 select I[n] else Self(n-1) + Self(n-3) + Self(n-4) + Self(n-5) + Self(n-6): n in [1..30]]; // G. C. Greubel, Jan 09 2018

Crossrefs

Sequence in context: A137354 A113495 A110997 * A376853 A161328 A073141

Adjacent sequences: A001637 A001638 A001639 * A001641 A001642 A001643

Keyword

nonn

Author

N. J. A. Sloane

Status

approved