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A224330
Number of idempotent n X n 0..5 matrices of rank n-1.
1
1, 22, 213, 1724, 12955, 93306, 653177, 4478968, 30233079, 201553910, 1330255861, 8707129332, 56596340723, 365699432434, 2350924922865, 15045919506416, 95917736853487, 609359740010478, 3859278353399789, 24374389600419820
OFFSET
1,2
COMMENTS
Column 5 of A224333.
FORMULA
a(n) = n*(2*6^(n-1) - 1).
a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3) - 36*a(n-4).
G.f.: x*(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2). - Colin Barker, Aug 29 2018
EXAMPLE
Some solutions for n=3:
0 5 0 1 0 0 1 0 0 0 0 0 0 3 3 0 0 0 1 5 0
0 1 0 0 1 2 5 0 1 4 1 0 0 1 0 3 1 0 0 0 0
0 0 1 0 0 0 0 0 1 2 0 1 0 0 1 1 0 1 0 4 1
MATHEMATICA
Table[n*(2*6^(n-1)-1), {n, 1, 40}] (* or *)
CoefficientList[Series[(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2), {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *)
PROG
(PARI) Vec(x*(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018
CROSSREFS
Sequence in context: A125385 A126543 A232019 * A223928 A224052 A224305
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, formula from M. F. Hasler, William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013
STATUS
approved