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 A106510 Expansion of (1+x)^2/(1+x+x^2). 12
 1, 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, -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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums of the Riordan array ((1+x)/(1+x+x^2),x/(1+x)), A106509. Equals INVERT transform of (1, -2, 3, -4, 5, ...). - Gary W. Adamson, Oct 10 2008 LINKS Index entries for linear recurrences with constant coefficients, signature (-1,-1). FORMULA a(n) = Sum_{k=0..n} Sum_{j=0..n-k} (-1)^j*binomial(2n-k-j, j) a(n) = A049347(n-1) = A102283(n) if n >= 1. - R. J. Mathar, Aug 07 2011 From Michael Somos, Oct 15 2008: (Start) Euler transform of length 3 sequence [ 1, -2, 1]. a(n) is multiplicative with a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 3), a(p^e) = (-1)^e if p == 2 (mod 3). G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v) = 4 - 3*v - u * (4 - 2*v - u). (End) a(-n) = a(n). a(n+3) = a(n) unless n = 0 or n = -3. a(n) = Sum_{k=0..n} A128908(n,k)*(-1)^(n-k). - Philippe Deléham, Jan 22 2012 EXAMPLE 1 + x - x^2 + x^4 - x^5 + x^7 - x^8 + x^10 - x^11 + x^13 - x^14 + ... MATHEMATICA {1}~Join~LinearRecurrence[{-1, -1}, {1, -1}, 105] (* Jean-François Alcover, Oct 28 2019 *) PROG (PARI) {a(n) = if( n==0, 1, [0, 1, -1][n%3 + 1])} \\ Michael Somos, Oct 15 2008 (PARI) {a(n) = if( n==0, 1, kronecker(-3, n))} \\ Michael Somos, Oct 15 2008 (PARI) A106510(n)=kronecker(-3, n+!n) \\ M. F. Hasler, May 07 2018 CROSSREFS Sequence in context: A156707 A131309 A267208 * A163806 A163810 A163804 Adjacent sequences:  A106507 A106508 A106509 * A106511 A106512 A106513 KEYWORD easy,sign,mult AUTHOR Paul Barry, May 04 2005 EXTENSIONS Edited by M. F. Hasler, May 07 2018 STATUS approved

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Last modified February 24 10:11 EST 2020. Contains 332209 sequences. (Running on oeis4.)