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A224329 Number of idempotent n X n 0..4 matrices of rank n-1. 1
1, 18, 147, 996, 6245, 37494, 218743, 1249992, 7031241, 39062490, 214843739, 1171874988, 6347656237, 34179687486, 183105468735, 976562499984, 5187988281233, 27465820312482, 144958496093731, 762939453124980 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 4 of A224333.
LINKS
FORMULA
a(n) = n*(2*5^(n-1)-1).
a(n) = 12*a(n-1) - 46*a(n-2) + 60*a(n-3) - 25*a(n-4).
G.f.: x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2). - Colin Barker, Aug 29 2018
EXAMPLE
Some solutions for n=3:
..0..0..0....1..0..0....0..4..2....1..0..0....1..0..0....1..0..0....1..2..0
..3..1..0....0..1..2....0..1..0....1..0..3....0..1..3....0..0..0....0..0..0
..3..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..1
PROG
(PARI) Vec(x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018
CROSSREFS
Cf. A224333.
Sequence in context: A178759 A036397 A247741 * A221352 A271755 A197214
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, formula via M. F. Hasler William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013
STATUS
approved

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Last modified April 18 15:16 EDT 2024. Contains 371780 sequences. (Running on oeis4.)