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

 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!)
 A200562 Expansion of 1 / ((1 - 2*x) * (1 + 3*x + 4*x^2)) in powers of x. 1
 1, -1, 3, 3, -5, 35, -21, 51, 187, -253, 1035, -45, 91, 8099, -8277, 25203, 23035, -38845, 286539, -179949, 442267, 1490147, -2045205, 8563635, -732869, 1498499, 65544843, -68410797, 211488475, 176048675, -300358101, 2344363251, -1536690053, 3822551747, 11858974155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Index entries for linear recurrences with constant coefficients, signature (-1,2,8). FORMULA a(n) = -a(n-1) + 2*a(n-2) + 8*a(n-3) for all n in Z. 7*a(n) = 2^(n+1) +(-1)^n*( 5*A049072(n) -4*A049072(n-1) ). - R. J. Mathar, Nov 19 2011 a() = a(-n-3) * 2^(2*n+3) for all n in Z. - Michael Somos, Sep 17 2014 0 = a(n)*(+4*a(n+1) + 2*a(n+2)) + a(n+1)*(+a(n+1) + a(n+2)) for all n in Z. - Michael Somos, Sep 17 2014 EXAMPLE G.f. = 1 - x + 3*x^2 + 3*x^3 - 5*x^4 + 35*x^5 - 21*x^6 + 51*x^7 + 187*x^8 + ... MATHEMATICA LinearRecurrence[{-1, 2, 8}, {-1, 3, 3}, 40] (* Harvey P. Dale, Aug 03 2012 *) CoefficientList[Series[1/((1-2*x)*(1+3*x+4*x^2)), {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2018 *) PROG (PARI) {a(n) = if( n<0, polcoeff( x^3 / ((2 - x) * (4 + 3*x + x^2)) + x * O(x^-n), -n), polcoeff( 1 / ((1 - 2*x) * (1 + 3*x + 4*x^2)) + x * O(x^n), n))}; /* Michael Somos, Sep 17 2014 */ (PARI) x='x+O('x^50); Vec(1/((1-2*x)*(1+3*x+4*x^2))) \\ G. C. Greubel, Aug 13 2018 (Magma) m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1+3*x+4*x^2)))); // G. C. Greubel, Aug 13 2018 CROSSREFS Sequence in context: A265878 A201496 A110426 * A093310 A256402 A170919 Adjacent sequences: A200559 A200560 A200561 * A200563 A200564 A200565 KEYWORD sign,easy AUTHOR Krishnamurthy Balasubraniam, Nov 19 2011 EXTENSIONS Definition from R. J. Mathar, Nov 19 2011 Added a(0) = 1. - Michael Somos, Sep 17 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.

Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)