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 A130779 a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3. 8

%I

%S 1,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 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 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 a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.

%C Inverse binomial transform of A002522. - _R. J. Mathar_, Jun 13 2008

%C Multiplicative with a(2)=2, a(2^e)=0 if e>1, a(p^e)=0 for odd prime p if e>=1. Dirichlet g.f. 1+2^(1-s). - _R. J. Mathar_, Jun 28 2011

%C a(n-1) is the determinant of the symmetric n X n matrix M(i,j) = rad(gcd(i,j)) for 1 <= i, j <= n, where rad(n) is the largest squarefree number dividing n (A007947). - _Amiram Eldar_, Jul 19 2019

%D J. Sándor and B. Crstici, Handbook of Number Theory II, Kluwer, 2004, p. 265.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F G.f.: 1+x+2x^2.

%F a(n) = (C((n+2)^2,n+4) mod 2) + (C((n+1)^2,n+3) mod 2) + 2*(C(n^2,n+2) mod 2). - _Paolo P. Lava_, Dec 19 2007

%F a(n) = A167666(n,0). - _Philippe Deléham_, Feb 18 2012

%F a(n) = n! mod 3. - _Charles Kusniec_, Jan 25 2020

%t PadRight[{1,1,2},120,0] (* _Harvey P. Dale_, May 02 2015 *)

%t LinearRecurrence[{1},{1,1,2,0},105] (* _Ray Chandler_, Jul 15 2015 *)

%o (PARI) a(n)=if(n<3,max(n,1),0) \\ _Charles R Greathouse IV_, Dec 21 2011

%Y Cf. A002522, A007947, A130706, A167666.

%K nonn,mult,easy

%O 0,3

%A _Paul Curtz_, Jul 14 2007

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Last modified April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)