The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A257181 Expansion of (1 - x) * (1 + x^4) / (1 + x^5) in powers of x. 1
 1, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,-1). FORMULA Euler transform of length 10 sequence [-1, 0, 0, 1, -1, 0, 0, -1, 0, 1]. a(n) = a(-n) for all n in Z. a(n+5) = -a(n) unless n = 0 or -5. a(5*n) = 2 * (-1)^n unless n = 0. a(5*n + 2) = a(5*n + 3) = 0. a(5*n + 1) = a(5*n - 1) = -(-1)^n. G.f.: (1 - x) * (1 + x^4) / (1 + x^5). G.f.: (1 - x) * (1 - x^5) * (1 - x^8) / ((1 - x^4) * (1 - x^10)). Convolution inverse is A257179. a(n) = (-1)^floor( (n+4) / 5) * A164116(n). EXAMPLE G.f. = 1 - x + x^4 - 2*x^5 + x^6 - x^9 + 2*x^10 - x^11 + x^14 - 2*x^15 + ... MATHEMATICA a[ n_] := -Boole[n == 0] + {-1, 0, 0, 1, -2, 1, 0, 0, -1, 2}[[Mod[n, 10, 1]]]; a[ n_] := SeriesCoefficient[ (1 - x) * (1 + x^4) / (1 + x^5), {x, 0, Abs@n}]; CoefficientList[Series[(1-x)*(1+x^4)/(1+x^5), {x, 0, nmax}], x] (* G. C. Greubel, Aug 02 2018 *) PROG (PARI) {a(n) = if( n==0, 1, (-1)^(n\5) * [2, -1, 0, 0, 1][n%5 + 1])}; (PARI) {a(n) = polcoeff( (1 - x) * (1 + x^4) / (1 + x^5) + x * O(x^abs(n)), abs(n))}; (PARI) x='x+O('x^60); Vec((1-x)*(1+x^4)/(1+x^5)) \\ G. C. Greubel, Aug 02 2018 (MAGMA) m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1+x^4)/(1+x^5))); // G. C. Greubel, Aug 02 2018 CROSSREFS Cf. A164116, A257179. Sequence in context: A152815 A115296 A059048 * A164116 A164118 A180981 Adjacent sequences:  A257178 A257179 A257180 * A257182 A257183 A257184 KEYWORD sign,easy AUTHOR Michael Somos, Apr 17 2015 STATUS approved

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

Last modified June 18 04:41 EDT 2021. Contains 345098 sequences. (Running on oeis4.)