A001649 A Fielder sequence. (Formerly M2649 N1056)

1, 3, 7, 15, 26, 57, 106, 207, 403, 788, 1530, 2985, 5812, 11322, 22052, 42959, 83675, 162993, 317491, 618440, 1204651, 2346534, 4570791, 8903409, 17342876, 33782050, 65803777, 128178646, 249678140, 486346022, 947349461, 1845334319, 3594511719, 7001720167

Offset

1,2

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

Formula

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

Maple

A001649:=-(1+2*z+3*z**2+4*z**3+6*z**5)/(z+1)/(z**5-z**4+2*z**3-z**2+2*z-1); # [Conjectured by Simon Plouffe in his 1992 dissertation.]

Mathematica

LinearRecurrence[{1, 1, 1, 1, 0, 1}, {1, 3, 7, 15, 26, 57}, 50] (* T. D. Noe, Aug 09 2012 *)
CoefficientList[Series[x*(1+2*x+3*x^2+4*x^3+6*x^5)/(1-x-x^2-x^3-x^4-x^6), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *)

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+3*x^2+4*x^3+6*x^5)/(1-x-x^2-x^3-x^4-x^6)+x*O(x^n), n))
(Magma) I:=[1, 3, 7, 15, 26, 57]; [n le 6 select I[n] else Self(n-1) + Self(n-2) + Self(n-3) + Self(n-4) + Self(n-6): n in [1..30]]; // G. C. Greubel, Dec 19 2017

Crossrefs

Sequence in context: A131076 A001648 A051054 * A303220 A301894 A213215

Adjacent sequences: A001646 A001647 A001648 * A001650 A001651 A001652

Keyword

nonn

Author

N. J. A. Sloane

Status

approved