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).

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).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

Cf. A114358, A114360, A114361.

Sequence in context: A252061 A031707 A158403 * A038013 A334183 A078144

Adjacent sequences: A114356 A114357 A114358 * A114360 A114361 A114362

Keyword

nonn,easy

Author

Benoit Cloitre, Feb 09 2006

Status

approved