

A094943


A sequence generated from a semimagic square.


2



1, 13, 72, 429, 2601, 15534, 93339, 559845, 3359232, 20155473, 120932109, 725594598, 4353563943, 26121388761, 156728328192, 940369966965, 5642219821473, 33853318876350, 203119913356515, 1218719480001309
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OFFSET

1,2


COMMENTS

The 3 rows: 1 3 2, 2 1 3 and 3 2 1 form a semimagic square; with rows, columns and a diagonal having a sum of 6. a(n)/a(n1) tends to 6, an eigenvalue of the matrix. E.g.: a(7)/a(6) = 93339/15534 = 6.0086... A094944 uses the same format and operations but has different terms.


LINKS



FORMULA

G.f.: (1+10*x+18*x^2)/(13*x18*x^315*x^2); a(n+3)=3*a(n+2)+15*a(n+1)+18*a(n), a(0) = 1, a(1) = 13, a(2) = 72.  Alec Mihailovs, Aug 28 2005
Let [1 3 2 / 2 1 3 / 3 2 1] = the 3 X 3 matrix M. Take M^n * [1 0 0] = [p q r]; then a(n) = p.


EXAMPLE

a(4) = 429 since M^4 * [1 0 0] = [429 q r]


MATHEMATICA

a[n_] := (MatrixPower[{{1, 3, 2}, {2, 1, 3}, {3, 2, 1}}, n].{{1}, {0}, {0}})[[1, 1]]; Table[ a[n], {n, 10}] (* Robert G. Wilson v, May 29 2004 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



