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A224524 Table read by antidiagonals: T(n,k) is the number of idempotent n X n 0..k matrices of rank 1. 5
1, 1, 6, 1, 10, 27, 1, 14, 69, 108, 1, 18, 123, 404, 405, 1, 22, 195, 892, 2155, 1458, 1, 26, 273, 1716, 5845, 10830, 5103, 1, 30, 375, 2732, 13525, 36042, 52241, 17496, 1, 34, 477, 4324, 24575, 99774, 213647, 244648, 59049, 1, 38, 603, 6060, 44545, 208146, 705215 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

      1,      1,      1,      1,      1,     1,    1,   1,  1, 1, ...

      6,     10,     14,     18,     22,    26,   30,  34, 38, ...

     27,     69,    123,    195,    273,   375,  477, 603, ...

    108,    404,    892,   1716,   2732,  4324, 6060, ...

    405,   2155,   5845,  13525,  24575, 44545, ...

   1458,  10830,  36042,  99774, 208146, ...

   5103,  52241, 213647, 705215, ...

  17496, 244648, ...

  59049, ...

  ...

LINKS

Robert Israel, Table of n, a(n) for n = 1..10011

EXAMPLE

Some solutions for n=3, k=4:

  1 0 0   0 4 4   0 0 0   0 4 2   1 2 1   0 0 0   0 1 0

  0 0 0   0 1 1   3 1 0   0 0 0   0 0 0   0 0 0   0 1 0

  1 0 0   0 0 0   0 0 0   0 2 1   0 0 0   1 4 1   0 0 0

MAPLE

f:= proc(n, k)

  local tot, a1, a0, a2, m, u;

  tot:= 0;

  for a1 from 1 to n do

    for a0 from 0 to n-a1 do

      a2:= n-a1-a0;

      if a0 = 0 then tot:= tot + n!/(a1!*a2!)*a1*(k-1)^a2

      elif a2 = 0 then tot:= tot + n!/(a0!*a1!)*a1*(k+1)^a0

      else

        u:= n!/(a0!*a1!*a2!)*a1;

        for m from 2 to k do

          tot:= tot + u*((m-1)^a2 - (m-2)^a2)*(floor(k/m)+1)^a0

        od

      fi

  od od;

  tot

end proc:

seq(seq(f(i, j-i), i=1..j-1), j=2..20); # Robert Israel, Dec 15 2019

CROSSREFS

Column 1 is A027471(n+1).

Sequence in context: A127142 A224333 A259671 * A348982 A046618 A328898

Adjacent sequences:  A224521 A224522 A224523 * A224525 A224526 A224527

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 09 2013

STATUS

approved

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Last modified January 20 08:47 EST 2022. Contains 350467 sequences. (Running on oeis4.)