cp's OEIS Frontend

A114698 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).

%I A114698 #16 Nov 30 2014 03:06:48
%S A114698 1,18,38,58,78,98,118,138,158,178,198,218,238,258,278,298,318,338,358,
%T A114698 378,398,418,438,458,478,498,518,538,558,578,598,618,638,658,678,698,
%U A114698 718,738,758,778,798,818,838,858,878,898,918,938,958,978,998,1018,1038
%N A114698 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 A114698 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 A114698 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 A114698 a(1)=1 then a(n)=20n-22.
%F A114698 (Conjecture) G.f.: F(x)=(1+16*x+3*x^2)/(1-x)^2. - _L. Edson Jeffery_, Jan 21 2012
%F A114698 (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 A114698 (PARI) a(n)=if(n<2,1,20*n-22)
%Y A114698 Cf. A016921, A114646.
%K A114698 nonn
%O A114698 1,2
%A A114698 _Benoit Cloitre_, Feb 09 2006