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A001641 A Fielder sequence: a(n) = a(n-1) + a(n-2) + a(n-4).
(Formerly M2364 N0935)
2
1, 3, 4, 11, 16, 30, 50, 91, 157, 278, 485, 854, 1496, 2628, 4609, 8091, 14196, 24915, 43720, 76726, 134642, 236283, 414645, 727654, 1276941, 2240878, 3932464, 6900996, 12110401, 21252275, 37295140, 65448411, 114853952, 201554638, 353703730, 620706779 (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).

FORMULA

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

a(n) = n*Sum_{k=1..n} Sum_{j=floor((4*k-n)/3)..floor((4*k-n)/2)} binomial(j,n-4*k+3*j)*binomial(k,j))/k. - Vladimir Kruchinin, May 25 2011

MAPLE

A001641:=-(1+2*z+4*z**3)/(z+1)/(z**3-z**2+2*z-1); # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

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

PROG

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

(Maxima) a(n):=(sum(sum(binomial(j, n-4*k+3*j)*binomial(k, j), j, floor((4*k-n)/3), floor((4*k-n)/2))/k, k, 1, n))*n; /* Vladimir Kruchinin, May 25 2011 */

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

CROSSREFS

Cf. A060945.

Sequence in context: A290493 A266384 A248825 * A007382 A127804 A027306

Adjacent sequences:  A001638 A001639 A001640 * A001642 A001643 A001644

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)