login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053537 Expansion of 1/((1+5*x)*(1-15*x)). 2
1, 10, 175, 2500, 38125, 568750, 8546875, 128125000, 1922265625, 28832031250, 432490234375, 6487304687500, 97309814453125, 1459645996093750, 21894696044921875, 328420410156250000, 4926306304931640625, 73894593811035156250, 1108418910980224609375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..845

Index entries for linear recurrences with constant coefficients, signature (10,75).

FORMULA

a(n) = (5^n/4)*(3^(n+1) + (-1)^n).

a(n) = 10*a(n-1) + 75*a(n-2), with a(0)=1, a(1)=10.

E.g.f.: (3*exp(15*x) + exp(-5*x))/4. - G. C. Greubel, May 16 2019

MATHEMATICA

LinearRecurrence[{10, 75}, {1, 10}, 30] (* G. C. Greubel, May 16 2019 *)

CoefficientList[Series[1/((1+5x)(1-15x)), {x, 0, 20}], x] (* Harvey P. Dale, Jun 15 2022 *)

PROG

(PARI) Vec(1/((1+5*x)*(1-15*x)) + O(x^30)) \\ Michel Marcus, Dec 03 2014

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/((1+5*x)*(1-15*x)) )); // G. C. Greubel, May 16 2019

(Sage) (1/((1+5*x)*(1-15*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

(GAP) a:=[1, 10];; for n in [3..30] do a[n]:=10*a[n-1]+75*a[n-2]; od; a; # G. C. Greubel, May 16 2019

CROSSREFS

Cf. A015518.

Sequence in context: A304445 A268936 A144516 * A049380 A302105 A200060

Adjacent sequences: A053534 A053535 A053536 * A053538 A053539 A053540

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 15 2000

EXTENSIONS

Terms a(11) onward added by G. C. Greubel, May 16 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 01:31 EST 2022. Contains 358431 sequences. (Running on oeis4.)