A114361 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)^(-9).

1, 5778, 40169, 87727, 136338, 184958, 233578, 282198, 330818, 379438, 428058, 476678, 525298, 573918, 622538, 671158, 719778, 768398, 817018, 865638, 914258, 962878, 1011498, 1060118, 1108738, 1157358, 1205978, 1254598, 1303218, 1351838

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..30.

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

Formula

a(n) = 48620n-106762, with n>4, a(1)=1, a(2)=5778, a(3)=40169, a(4)=87727.

From Colin Barker, Mar 18 2012: (Start)

a(n) = 2*a(n-1)-a(n-2) for n>6.

G.f.: x*(1+5776*x+28614*x^2+13167*x^3+1053*x^4+9*x^5)/(1-x)^2. (End)

Mathematica

Rest@ CoefficientList[Series[x (1 + 5776 x + 28614 x^2 + 13167 x^3 + 1053 x^4 + 9 x^5)/(1 - x)^2, {x, 0, 30}], x] (* Michael De Vlieger, Feb 22 2021 *)

Crossrefs

Cf. A114358, A114359, A114360.

Sequence in context: A031574 A004953 A004973 * A235086 A098476 A248132

Adjacent sequences: A114358 A114359 A114360 * A114362 A114363 A114364

Keyword

nonn,easy

Author

Benoit Cloitre, Feb 09 2006

Status

approved