login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001645 A Fielder sequence.
(Formerly M2626 N1041)
1
1, 3, 7, 11, 26, 45, 85, 163, 304, 578, 1090, 2057, 3888, 7339, 13862, 26179, 49437, 93366, 176321, 332986, 628852, 1187596, 2242800, 4235569, 7998951, 15106172, 28528288, 53876211, 101746240, 192149690, 362878313, 685302531, 1294206745, 2444133829 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

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

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.

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

FORMULA

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

MAPLE

A001645:=-(1+2*z+3*z**2+5*z**4)/(-1+z+z**2+z**3+z**5); [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

LinearRecurrence[{1, 1, 1, 0, 1}, {1, 3, 7, 11, 26}, 50] (* T. D. Noe, Aug 09 2012 *)

CoefficientList[Series[x*(1+2*x+3*x^2+5*x^4)/(1-x-x^2-x^3-x^5), {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+5*x^4)/(1-x-x^2-x^3-x^5)+x*O(x^n), n))

(MAGMA) I:=[1, 3, 7, 11, 26]; [n le 5 select I[n] else Self(n-1) + Self(n-2) + Self(n-3) + Self(n-5): n in [1..30]]; // G. C. Greubel, Dec 19 2017

CROSSREFS

Sequence in context: A316962 A092284 A024459 * A103798 A093361 A227364

Adjacent sequences:  A001642 A001643 A001644 * A001646 A001647 A001648

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)