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Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-3).
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%I #16 Nov 30 2014 03:06:48

%S 1,18,38,58,78,98,118,138,158,178,198,218,238,258,278,298,318,338,358,

%T 378,398,418,438,458,478,498,518,538,558,578,598,618,638,658,678,698,

%U 718,738,758,778,798,818,838,858,878,898,918,938,958,978,998,1018,1038

%N Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-3).

%C More generally for any n>=floor((m+1)/2) the trace of M(n)^(-m) = binomial(2*m,m)*n-2^(2*m-1)+binomial(2*m-1,m).

%H S. Barbero, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Barbero/barbero15.html">Dickson Polynomials, Chebyshev Polynomials, and Some Conjectures of Jeffery</a>, Journal of Integer Sequences, 17 (2014), #14.3.8.

%F a(1)=1 then a(n)=20n-22.

%F (Conjecture) G.f.: F(x)=(1+16*x+3*x^2)/(1-x)^2. - _L. Edson Jeffery_, Jan 21 2012

%F (Conjecture) a(n)=2*a(n-1)-a(n-2), n>1, a(0)=1, a(1)=18. - _L. Edson Jeffery_, Jan 21 2012

%o (PARI) a(n)=if(n<2,1,20*n-22)

%Y Cf. A016921, A114646.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Feb 09 2006