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 A224331 Number of idempotent n X n 0..6 matrices of rank n-1. 1
 1, 26, 291, 2740, 24005, 201678, 1647079, 13176680, 103766409, 807072130, 6214455467, 47455841820, 359873467213, 2712892291382, 20346692185455, 151921968318160, 1129919639366417, 8374698503539434, 61879716720597043 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 6 of A224333. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Index entries for linear recurrences with constant coefficients, signature (16,-78,112,-49). FORMULA a(n) = n*(2*7^(n-1)-1). a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4). G.f.: x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2). - Colin Barker, Aug 29 2018 EXAMPLE Some solutions for n=3: ..1..5..0....0..3..6....1..0..0....0..0..0....1..0..0....1..0..0....0..0..0 ..0..0..0....0..1..0....0..1..0....6..1..0....0..1..0....0..1..0....2..1..0 ..0..2..1....0..0..1....0..0..0....4..0..1....1..6..0....3..4..0....3..0..1 MATHEMATICA Table[n*(2*7^(n-1)-1), {n, 1, 40}] (* or *) CoefficientList[Series[(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) , {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *) PROG (PARI) Vec(x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018 CROSSREFS Cf. A224333. Sequence in context: A336732 A227332 A020925 * A125414 A208600 A010831 Adjacent sequences: A224328 A224329 A224330 * A224332 A224333 A224334 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 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)