A114360 - OEIS

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).

1, 2207, 12389, 25147, 38017, 50887, 63757, 76627, 89497, 102367, 115237, 128107, 140977, 153847, 166717, 179587, 192457, 205327, 218197, 231067, 243937, 256807, 269677, 282547, 295417, 308287, 321157, 334027, 346897, 359767, 372637, 385507

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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).

LINKS

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

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

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]

MATHEMATICA

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 *)

CROSSREFS

Cf. A114358, A114359, A114361.

Sequence in context: A004951 A004971 A037210 * A023319 A207793 A232074

Adjacent sequences: A114357 A114358 A114359 * A114361 A114362 A114363

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Feb 09 2006

STATUS

approved