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A174577 Expansion: -1/(-1 + x^2 + x^3 - x^7 + x^8 - x^10) 2
1, 0, 1, 1, 1, 2, 2, 2, 5, 3, 6, 8, 7, 13, 14, 15, 27, 24, 35, 49, 47, 75, 88, 97, 152, 159, 208, 289, 304, 435, 537, 609, 877, 1000, 1253, 1703, 1914, 2565, 3241, 3776, 5146, 6155, 7595, 10090, 11846, 15306, 19487, 23217, 30543, 37488, 46119, 60120, 72552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

The limiting ratio is:1.2520730782144198.

The application of modular form theory to the Padovan polynomial: using McKean and Moll definition on the Padovan minimal Pisot polynomial:

f(-1/x)=x^(2*n)*f(x);

f(x)=x^3-x-1;

p(x)=x^3*f(-1/x) - x^(3 + 4)*f(x)=-1 + x^2 - x^3 + x^7 + x^8 - x^10;

which has the above root ratio: the expansion is of the toral inverse polynomial times -1.

REFERENCES

McKean and Moll, Elliptic Curves, Function Theory,Geometry, Arithmetic, Cambridge University Press, New York, 199, page 173

LINKS

Table of n, a(n) for n=0..52.

MATHEMATICA

f[x_] = x^3 - x - 1;

p[x_] = ExpandAll[x^3*f[-1/x] - x^(3 + 4)*f[x]];

f[x_] = ExpandAll[x^10*p[1/x]]

a = Table[SeriesCoefficient[

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

PROG

(PARI) Vec(1/(1-x^2-x^3+x^7-x^8+x^10)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Cf. A115346, A000931.

Sequence in context: A115253 A154429 A333388 * A194684 A076737 A246119

Adjacent sequences:  A174574 A174575 A174576 * A174578 A174579 A174580

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Nov 29 2010

STATUS

approved

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Last modified September 20 01:54 EDT 2020. Contains 337260 sequences. (Running on oeis4.)