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).

1, 47, 117, 187, 257, 327, 397, 467, 537, 607, 677, 747, 817, 887, 957, 1027, 1097, 1167, 1237, 1307, 1377, 1447, 1517, 1587, 1657, 1727, 1797, 1867, 1937, 2007, 2077, 2147, 2217, 2287, 2357, 2427, 2497, 2567, 2637, 2707, 2777, 2847, 2917, 2987, 3057

Offset: 1

Author

Benoit Cloitre, Feb 09 2006

Keywords

• nonn
• easy

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).

Links

• S. Barbero, Dickson Polynomials, Chebyshev Polynomials, and Some Conjectures of Jeffery, Journal of Integer Sequences, 17 (2014), #14.3.8
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Programs

PARI

a(n)=if(n<2,1,70*n-93)

Formula

a(1)=1 then a(n)=70n-93.

(Conjecture) G.f.: F(x)=x*(1+45*x+24*x^2)/(1-x)^2. - L. Edson Jeffery, Jan 21 2012

(Conjecture) a(n)=2*a(n-1)-a(n-2), n>1, a(1)=1, a(2)=47. - L. Edson Jeffery, Jan 21 2012