The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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, 1232504, 1120599, 196830 (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 MATHEMATICA Unprotect[Power]; 0^0 = 1; Protect[Power]; f[n_, k_] := Module[{tot, a1, a0, a2, m, u}, tot = 0; For[a1 = 1, a1 <= n, a1++, For[a0 = 0, a0 <= n - a1, a0++, a2 = n - a1 - a0; Which[a0 == 0, tot = tot + n!/(a1!*a2!)*a1*(k - 1)^a2, a2 == 0, tot = tot + n!/(a0!*a1!)*a1*(k + 1)^a0, True, u = n!/(a0!*a1!*a2!)*a1; For[m = 2, m <= k, m++, tot = tot + u*((m - 1)^a2 - (m - 2)^a2)*(Floor[k/m] + 1)^a0]]]]; tot]; Table[Table[f[i, j - i], {i, 1, j - 1}], {j, 2, 20}] // Flatten (* Jean-François Alcover, Feb 04 2023, after Robert Israel *) CROSSREFS Column 1 is A027471(n+1). Sequence in context: A127142 A224333 A259671 * A348982 A350677 A046618 Adjacent sequences: A224521 A224522 A224523 * A224525 A224526 A224527 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 09 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 13 20:16 EDT 2024. Contains 371645 sequences. (Running on oeis4.)