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A174650 Expansion of 1 / (1 - x - x^2 + x^3 - x^5 + x^15 - x^17 - x^18 + x^19 + x^20). 1
1, 1, 2, 2, 3, 4, 6, 9, 13, 19, 27, 39, 56, 81, 117, 168, 242, 348, 503, 725, 1046, 1506, 2169, 3124, 4501, 6487, 9348, 13471, 19409, 27965, 40293, 58058, 83657, 120540, 173684, 250255, 360589, 519568, 748642, 1078708, 1554291, 2239548, 3226923, 4649623 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limiting ratio is: 1.4408839873261408 ... .

Using McKean and Moll modular form definition on 1 - x^2 + x^3 + x^4 - x^5;

Pisot polynomial at n=5 level: f(-1/x)=x^(2*n)*f(x).

On Nov 30 2010 the author wrote: The McKean-Moll modular form formula is: f(-1/w)=w^(2*n)*f(w). What I did was make a toral inverse like for: m the power of the polynomial in question; w^m*f(-1/m)=w^(2*n+m)*f(w). Setting that result equal to zero derives the polynomials. Their toral inverses are used to get the expansion sequences.

REFERENCES

Henry McKean and Victor Moll, Elliptic Curves - Function Theory, Geometry, Arithmetic. Cambridge University Press, New York, 1999, page 173 (ISBN-13: 978-0521658171).

LINKS

Georg Fischer, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: 1 / ( (x-1)*(1+x)*(x^18+x^17+x^13+x^11+x^9+x^7+x^5+x-1) ).

MATHEMATICA

f[x_] = 1 - x^2 + x^3 + x^4 - x^5;

p[x_] = ExpandAll[x^5*f[-1/x] - x^(5 + 10)*f[x]];

f[x_] = ExpandAll[x^20*p[1/x]]

a = Table[SeriesCoefficient[

      Series[1/f[x], {x, 0, 100}], n], {n, 0, 100}]

(* or *) LinearRecurrence[{1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, -1, -1}, {1, 1, 2, 2, 3, 4, 6, 9, 13, 19, 27, 39, 56, 81, 117, 168, 242, 348, 503, 725}, 1001] (* Georg Fischer, signature from Colin Barker, Feb 28 2019 *)

CROSSREFS

Cf. A107293, A174577.

Sequence in context: A157876 A289433 A212264 * A107293 A001611 A214448

Adjacent sequences:  A174647 A174648 A174649 * A174651 A174652 A174653

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Nov 29 2010

STATUS

approved

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Last modified November 14 12:44 EST 2019. Contains 329116 sequences. (Running on oeis4.)