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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 5 of A224333. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Index entries for linear recurrences with constant coefficients, signature (14,-61,84,-36). 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 Adjacent sequences:  A224327 A224328 A224329 * A224331 A224332 A224333 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

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Last modified September 25 22:38 EDT 2020. Contains 337346 sequences. (Running on oeis4.)