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A114359 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)^(-7). 4

%I

%S 1,843,3827,7252,10684,14116,17548,20980,24412,27844,31276,34708,

%T 38140,41572,45004,48436,51868,55300,58732,62164,65596,69028,72460,

%U 75892,79324,82756,86188,89620,93052,96484,99916,103348,106780,110212,113644

%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)^(-7).

%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 Harvey P. Dale, <a href="/A114359/b114359.txt">Table of n, a(n) for n = 1..1000</a>

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

%F a(n) = 3432*n - 6476 for n > 3; a(1)=1, a(2)=843, a(3)=3827.

%F From _Colin Barker_, Mar 18 2012: (Start)

%F a(n) = 2*a(n-1) - a(n-2) for n > 5.

%F G.f.: x*(1 + 841*x + 2142*x^2 + 441*x^3 + 7*x^4)/(1-x)^2. (End)

%t Join[{1,843,3827},LinearRecurrence[{2,-1},{7252,10684},40]] (* _Harvey P. Dale_, Nov 28 2014 *)

%Y Cf. A114358, A114360, A114361.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Feb 09 2006

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Last modified May 28 07:30 EDT 2022. Contains 354112 sequences. (Running on oeis4.)