The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A219977 Expansion of 1/(1+x+x^2+x^3). 7
 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani, Non-overlapping matrices, arXiv:1601.07723 [cs.DM], 2016. Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785, 2016 Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016. Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1). FORMULA G.f.: 1/(1 +x +x^2 +x^3). Euler transform of length 4 sequence [ -1, 0, 0, 1]. - Michael Somos, Dec 12 2012 a(n) = a(n+4) = -a(1-n). |a(n)| = A133872(n). REVERT transform is A036765. INVERT transform is A077962. - Michael Somos, Dec 12 2012 A038505(n+2) = p(-1) where p(x) is the unique degree-n polynomial such that p(k) = a(k) for k = 0, 1, ..., n. - Michael Somos, Dec 12 2012 From Wesley Ivan Hurt, Apr 22 2015: (Start) a(n) +a(n-1) +a(n-2) +a(n-3) = 0. a(n) = (-1)^n/2 +(-1)^(n/2 +1/4 -(-1)^n/4)/2. (End) EXAMPLE G.f. = 1 - x + x^4 - x^5 + x^8 - x^9 + x^12 - x^13 + x^16 - x^17 + x^20 - x^21 + ... MATHEMATICA CoefficientList[Series[1/(1+x+x^2+x^3), {x, 0, 80}], x] (* or *) PadRight[{}, 120, {1, -1, 0, 0}] LinearRecurrence[{-1, -1, -1}, {1, -1, 0}, 80] (* Harvey P. Dale, May 22 2021 *) PROG (PARI) {a(n) = [1, -1, 0, 0][n%4 + 1]} /* Michael Somos, Dec 12 2012 */ (PARI) Vec(1/(1+x+x^2+x^3) + O(x^100)) \\ Michel Marcus, Jan 28 2016 (Magma) m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1+x+x^2+x^3))); // Vincenzo Librandi, Apr 22 2015 CROSSREFS Cf. A036765, A038505, A049347, A077962, A133872. Sequence in context: A125999 A073784 A320006 * A128130 A133872 A286903 Adjacent sequences: A219974 A219975 A219976 * A219978 A219979 A219980 KEYWORD sign,easy AUTHOR Harvey P. Dale, Dec 02 2012 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 May 20 10:34 EDT 2024. Contains 372712 sequences. (Running on oeis4.)