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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
1, 843, 3827, 7252, 10684, 14116, 17548, 20980, 24412, 27844, 31276, 34708, 38140, 41572, 45004, 48436, 51868, 55300, 58732, 62164, 65596, 69028, 72460, 75892, 79324, 82756, 86188, 89620, 93052, 96484, 99916, 103348, 106780, 110212, 113644
OFFSET
1,2
COMMENTS
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).
FORMULA
a(n) = 3432*n - 6476 for n > 3; a(1)=1, a(2)=843, a(3)=3827.
From Colin Barker, Mar 18 2012: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 5.
G.f.: x*(1 + 841*x + 2142*x^2 + 441*x^3 + 7*x^4)/(1-x)^2. (End)
MATHEMATICA
Join[{1, 843, 3827}, LinearRecurrence[{2, -1}, {7252, 10684}, 40]] (* Harvey P. Dale, Nov 28 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Feb 09 2006
STATUS
approved