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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253442 Expansion of x * (96 - 816*x) / ((1 - x) * (1 - 1442*x + x^2)) in powers of x. 1
96, 137712, 198579888, 286352060064, 412919472031680, 595429592317621776, 858609059202538568592, 1238113667940468298287168, 1785359050561096083591526944, 2574486512795432612070683565360, 3712407766091963265509842109721456 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The continued fraction convergents of sqrt(10) are 3/1, 19/6, 117/37, 721/228, ...
LINKS
FORMULA
G.f.: x * (96 - 816*x) / ((1 - x) * (1 - 1442*x + x^2)).
a(n) = A253410(2*n) for all n in Z.
1 - a(-n) = A253410(2*n + 1) for all n in Z.
From Colin Barker, Nov 24 2017: (Start)
a(n) = (1/2 - (5+2*sqrt(10))/20*(721+228*sqrt(10))^(-n) + (-1/4 + 1/sqrt(10))*(721+228*sqrt(10))^n).
a(n) = 1443*a(n-1) - 1443*a(n-2) + a(n-3) for n>3.
(End)
EXAMPLE
G.f. = 96*x + 137712*x^2 + 198579888*x^3 + 286352060064*x^4 + ...
MATHEMATICA
CoefficientList[Series[48*x*(2-17*x)/((1-x)*(1-1442*x+x^2)), {x, 0, 30}], x] (* G. C. Greubel, Aug 03 2018 *)
LinearRecurrence[{1443, -1443, 1}, {96, 137712, 198579888}, 20] (* Harvey P. Dale, Aug 23 2020 *)
PROG
(PARI) {a(n) = my(t=(721 - 228*quadgen(40))^n); (1 - real(t) - 4*imag(t)) / 2};
(PARI) Vec(48*x*(2 - 17*x) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^20)) \\ Colin Barker, Nov 24 2017
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(48*x*(2 - 17*x)/((1 - x)*(1 - 1442*x + x^2)))); // G. C. Greubel, Aug 03 2018
CROSSREFS
Cf. A253410.
Sequence in context: A296061 A340396 A202929 * A159416 A008702 A133402
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Dec 31 2014
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 March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)