A114698 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)^(-3).

1, 18, 38, 58, 78, 98, 118, 138, 158, 178, 198, 218, 238, 258, 278, 298, 318, 338, 358, 378, 398, 418, 438, 458, 478, 498, 518, 538, 558, 578, 598, 618, 638, 658, 678, 698, 718, 738, 758, 778, 798, 818, 838, 858, 878, 898, 918, 938, 958, 978, 998, 1018, 1038

Offset: 1

Author

Benoit Cloitre, Feb 09 2006

Keywords

• nonn

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.

Crossrefs

Cf. A016921, A114646.

Programs

PARI

a(n)=if(n<2,1,20*n-22)

Formula

a(1)=1 then a(n)=20n-22.

(Conjecture) G.f.: F(x)=(1+16*x+3*x^2)/(1-x)^2. - L. Edson Jeffery, Jan 21 2012

(Conjecture) a(n)=2*a(n-1)-a(n-2), n>1, a(0)=1, a(1)=18. - L. Edson Jeffery, Jan 21 2012