This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A154955 #58 Dec 17 2024 10:12:36
%S A154955 1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A154955 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A154955 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A154955 a(1) = 1, a(2) = -1, followed by 0, 0, 0, ... .
%C A154955 Matrix inverse of A000012.
%C A154955 Moebius transform of the sequence A000035. Dirichlet inverse of A209229. Partial sums of a(n) is characteristic function of 1 (A063524). a(n)=(-1)^(n+1)*A019590(n). a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), a(n) = Sum_{d|n} b(d)*c(n/d): a(n) = A000012(n) * A092673(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000012(n) = A000035(n), a(n) * A000027(n) = A026741(n), a(n) * A008683(n) = A092673(n), a(n) * A036987(n-1) = A063524(n), a(n) * A000005(n) = A001227(n). - _Jaroslav Krizek_, Mar 21 2009
%C A154955 The Kn21 sums, see A180662, of triangle A108299 equal the terms of this sequence. - _Johannes W. Meijer_, Aug 14 2011
%C A154955 {a(n-1)}_{n>=1}, gives the alternating row sums of A132393. - _Wolfdieter Lang_, May 09 2017
%C A154955 With offset 0 the alternating row sums of A097805. - _Peter Luschny_, Sep 07 2017
%H A154955 Antti Karttunen, <a href="/A154955/b154955.txt">Table of n, a(n) for n = 1..10000</a>
%H A154955 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A154955 G.f.: A(x) = x - x^2 = x / (1 + x / (1 - x)). - _Michael Somos_, Jan 03 2013
%F A154955 a(n) = (2/sqrt(3))*sin((2*Pi/3)*n!). - _Lorenzo Pinlac_, Jan 16 2022
%F A154955 a(n) = [n = 1] - [n = 2], where [] is the Iverson bracket. - _Wesley Ivan Hurt_, Jun 22 2024
%F A154955 Multiplicative with a(2) = -1, a(2^e) = 0 if e > 1, a(p^e) = 0 if p > 2. - _Antti Karttunen_, Dec 17 2024
%t A154955 Join[{1, -1}, 0 Range[3, 100]] (* _Wesley Ivan Hurt_, Jun 22 2024 *)
%t A154955 PadRight[{1,-1},120,0] (* _Harvey P. Dale_, Dec 10 2024 *)
%o A154955 (PARI) A154955(n)=(n==1)-(n==2) \\ _M. F. Hasler_, Jan 13 2012
%Y A154955 Cf. A019590 (absolute values).
%Y A154955 Cf. A000005, A000012, A000027, A000035, A001227, A008683, A019590, A026741, A036987, A063524, A092673.
%Y A154955 Cf. A097805, A108299, A132393, A180662.
%K A154955 mult,sign,easy
%O A154955 1,1
%A A154955 _Mats Granvik_, Jan 18 2009
%E A154955 Keyword:mult added by _Antti Karttunen_, Dec 17 2024