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A114360 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)^(-8). 3

%I #16 Feb 23 2021 05:26:00

%S 1,2207,12389,25147,38017,50887,63757,76627,89497,102367,115237,

%T 128107,140977,153847,166717,179587,192457,205327,218197,231067,

%U 243937,256807,269677,282547,295417,308287,321157,334027,346897,359767,372637,385507

%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)^(-8).

%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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 12870*n-26333, with n> 3, a(1)=1, a(2)=2207, a(3)=12389.

%F a(n) = 2*a(n-1)-a(n-2) for n>5. G.f.: x*(1+2205*x+7976*x^2+2576*x^3+112*x^4)/(1-x)^2. [_Colin Barker_, Mar 18 2012]

%t Rest@ CoefficientList[Series[x (1 + 2205 x + 7976 x^2 + 2576 x^3 + 112 x^4)/(1 - x)^2, {x, 0, 32}], x] (* _Michael De Vlieger_, Feb 22 2021 *)

%Y Cf. A114358, A114359, A114361.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Feb 09 2006

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