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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 R. H. Hardin, Table of n, a(n) for n = 1..210 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 Adjacent sequences: A224326 A224327 A224328 * A224330 A224331 A224332 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.)