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 A224334 Number of idempotent 3 X 3 0..n matrices of rank 2. 3
 21, 51, 93, 147, 213, 291, 381, 483, 597, 723, 861, 1011, 1173, 1347, 1533, 1731, 1941, 2163, 2397, 2643, 2901, 3171, 3453, 3747, 4053, 4371, 4701, 5043, 5397, 5763, 6141, 6531, 6933, 7347, 7773, 8211, 8661, 9123, 9597, 10083, 10581, 11091, 11613, 12147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 3 of A224333. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 6*n^2 + 12*n + 3. From Colin Barker, Feb 23 2018: (Start) G.f.: 3*x*(7 - 4*x + x^2) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End) EXAMPLE Some solutions for n=3: ..1..2..0....1..0..0....1..0..0....1..0..1....1..0..2....0..0..0....0..0..0 ..0..0..0....1..0..2....0..1..0....0..1..3....0..1..2....3..1..0....1..1..0 ..0..1..1....0..0..1....0..0..0....0..0..0....0..0..0....1..0..1....2..0..1 PROG (PARI) a(n) = 6*n^2 + 12*n + 3 \\ Charles R Greathouse IV, Jun 17 2017 (PARI) Vec(3*x*(7 - 4*x + x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Feb 23 2018 CROSSREFS Cf. A224333. Sequence in context: A235884 A053178 A166150 * A305002 A242236 A235877 Adjacent sequences: A224331 A224332 A224333 * A224335 A224336 A224337 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 September 9 10:46 EDT 2024. Contains 375764 sequences. (Running on oeis4.)