This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A260190 Kronecker symbol(-6 / 2*n + 1). 4
 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1). FORMULA Euler transform of length 12 sequence [ 0, 1, 1, -1, 0, -2, 0, 0, 0, 0, 0, 1]. G.f.: (1 + x^3) / (1 - x^2 + x^4). G.f.: 1 / (1 - x^2 / (1 - x / (1 + 2*x / ( 1 - x / (1 - x / (1 + x)))))). a(n) = (-1)^n * a(n+3) = -a(n+6) = a(5-n) = a(n+2) - a(n+4) for all n in Z. a(n) = A117441(n-2) = (-1)^n * A260192(n) = (-1)^n * A117441(n+1) = A109017(2*n + 1). a(n) + a(n+1) = A214438(n-1). a(2*n) = A010892(n). a(3*n + 1) = 0. a(3*n) = a(3*n + 2) = A057077(n). EXAMPLE G.f. = 1 + x^2 + x^3 + x^5 - x^6 - x^8 - x^9 - x^11 + x^12 + x^14 + x^15 + ... MATHEMATICA a[ n_] := KroneckerSymbol[ -6, 2 n + 1]; LinearRecurrence[{0, 1, 0, -1}, {1, 0, 1, 1}, 120] (* Harvey P. Dale, Jun 24 2018 *) PROG (PARI) {a(n) = kronecker( -6, 2*n + 1)}; (PARI) {a(n) = (-1)^(n\6) * [ 1, 0, 1][n%3 + 1]}; (PARI) {a(n) = if( n<3, n=5-n); polcoeff( (1 + x^3) / (1 - x^2 + x^4) + x * O(x^n), n)}; CROSSREFS Cf. A010892, A057077, A109017, A117441, A214438, A260192. Sequence in context: A141687 A305385 A204418 * A260192 A057078 A127245 Adjacent sequences:  A260187 A260188 A260189 * A260191 A260192 A260193 KEYWORD sign,easy AUTHOR Michael Somos, Jul 18 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 December 5 16:12 EST 2019. Contains 329753 sequences. (Running on oeis4.)