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A001643 A Fielder sequence.
(Formerly M2368 N0938)
2
1, 3, 4, 11, 21, 42, 71, 131, 238, 443, 815, 1502, 2757, 5071, 9324, 17155, 31553, 58038, 106743, 196331, 361106, 664183, 1221623, 2246918, 4132721, 7601259, 13980892, 25714875, 47297029, 86992802, 160004703, 294294531, 541292030, 995591267, 1831177831 (list; graph; refs; listen; history; text; internal format)
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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 1, 1, 1).

FORMULA

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

MAPLE

A001643:=-(1+2*z+4*z**3+5*z**4+6*z**5)/(z+1)/(z**3+z**2+z-1)/(z**2-z+1); [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

LinearRecurrence[{1, 1, 0, 1, 1, 1}, {1, 3, 4, 11, 21, 42}, 50] (* T. D. Noe, Aug 09 2012 *)

PROG

(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3+5*x^4+6*x^5)/(1-x-x^2-x^4-x^5-x^6)+x*O(x^n), n))

(MAGMA) I:=[1, 3, 4, 11, 21, 42]; [n le 6 select I[n] else Self(n-1) + Self(n-2) + Self(n-4) + Self(n-5) + Self(n-6): n in [1..30]]; // G. C. Greubel, Jan 09 2018

CROSSREFS

Sequence in context: A110865 A152982 A001642 * A247171 A005218 A219514

Adjacent sequences:  A001640 A001641 A001642 * A001644 A001645 A001646

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 22 22:18 EDT 2018. Contains 305673 sequences. (Running on oeis4.)