cp's OEIS Frontend

A114646 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)^(-4).

%I A114646 #20 Jun 13 2015 00:52:02
%S A114646 1,47,117,187,257,327,397,467,537,607,677,747,817,887,957,1027,1097,
%T A114646 1167,1237,1307,1377,1447,1517,1587,1657,1727,1797,1867,1937,2007,
%U A114646 2077,2147,2217,2287,2357,2427,2497,2567,2637,2707,2777,2847,2917,2987,3057
%N A114646 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)^(-4).
%C A114646 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 A114646 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
%H A114646 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A114646 a(1)=1 then a(n)=70n-93.
%F A114646 (Conjecture) G.f.: F(x)=x*(1+45*x+24*x^2)/(1-x)^2. - _L. Edson Jeffery_, Jan 21 2012
%F A114646 (Conjecture) a(n)=2*a(n-1)-a(n-2), n>1, a(1)=1, a(2)=47. - _L. Edson Jeffery_, Jan 21 2012
%o A114646 (PARI) a(n)=if(n<2,1,70*n-93)
%K A114646 nonn,easy
%O A114646 1,2
%A A114646 _Benoit Cloitre_, Feb 09 2006