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 A145201 Triangle read by rows: T(n,k) = S(n,k) mod n, where S(n,k) = Stirling numbers of the first kind. 1
 0, 1, 1, 2, 0, 1, 2, 3, 2, 1, 4, 0, 0, 0, 1, 0, 4, 3, 1, 3, 1, 6, 0, 0, 0, 0, 0, 1, 0, 4, 4, 1, 0, 2, 4, 1, 0, 0, 8, 0, 3, 0, 6, 0, 1, 0, 6, 0, 0, 5, 3, 0, 0, 5, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 6, 11, 6, 3, 6, 5, 6, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 8, 0, 0, 0, 0, 7, 5, 7, 7, 7, 7, 7 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The triangle T(n,k) contains many zeros. The distribution of nonzero entries is quite chaotic, but shows regular patterns, too, e.g.: 1) T(n,1) > 0 for n prime or n=4; T(n,1)=0 else 2) T(5k,k) > 0 for all k More generally, it seems that: 3) T(pk,k) > 0 for k>0 and primes p The following table depicts the zero (-) and nonzero (x) entries for the first 80 rows of the triangle: - xx x-x xxxx x---x -xxxxx x-----x -xxx-xxx --x-x-x-x -x--xx--xx x---------x ---xxxxxxxxx x-----------x -x----xxxxxxxx --x-x-x-x-x-x-x -----xxx-x-x-xxx x---------------x -----x-xxx-x-x-xxx x-----------------x ---x---xxxxx-x-xxxxx --x---x-x---x-x---x-x -x--------xxxx----xxxx x---------------------x -------x-xxx-xxx-xxx-xxx ----x---x---x---x---x---x -x----------xx--xx--xx--xx --------x-x-x-x-x-x-x-x-x-x ---x-----x--xxxxxxxxxxxxxxxx x---------------------------x -----x---x-x--xxxxxxxxxxxxxxxx x-----------------------------x -------------xxx-x-x-x-x-x-x-xxx --x-------x-x-x-------x-----x-x-x -x--------------xx--------------xx ----x-x---x---x-x-----x---x-x-x---x -----------x-x-xxxxx---x-x-x-x-xxxxx x-----------------------------------x -x----------------xxxx------------xxxx --x---------x-x---x-x-----x---x-x---x-x -------x---x---x-xxx-xxx---x-x-x-xxx-xxx x---------------------------------------x -----x-----x-x-x-x-xxx-xxx---x-x-x-xxx-xxx x-----------------------------------------x ---x---------x------xxxxxxxx-x-x-x-xxxxxxxxx --------x---x-x-x-x-x-x-x-x-x---x-x-x-x-x-x-x -x--------------------xxxxxxxx--------xxxxxxxx x---------------------------------------------x ---------------x-x---xxx-x-x-xxx-x-x--xx-x-x-xxx ------x-----x-----x-----x-----x-----x-----x-----x ---------x---x---x---x--xx---x--xx---x--xx---x--xx --x-------------x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x ---x-----------x--------xxxx-x-xxxxx---xxxxx-x-xxxxx x---------------------------------------------------x -----------------x-x-x-x-xxxxx-x-xxxxx-x-xxxxx-x-xxxxx ----x-----x---x---------x-----x---x---------x-----x---x -------x-----x-----------xxx-xxx--xx-xxx-xxx-xxx-xxx-xxx --x---------------x-x---------------x-x---------------x-x -x--------------------------xx--xx--xx--xx--xx--xx--xx--xx x---------------------------------------------------------x -----------x---x---x-x-x----xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x-----------------------------------------------------------x -x----------------------------xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx --------x-----x-----x-x-x-x-----x-----x-x-x-x-----x-----x-x-x-x -----------------------------xxx-x-x-x-x-x-x-x-x-x-x-x-x-x-x-xxx ----x-------x---x---x---x---x---x---x---x---x-------x---x---x---x -----x---------x-----x-x-x-x-x--xx-x---x-x---x-x-------x-x-x---xxx x-----------------------------------------------------------------x ---x---------------x------------xxxx-------------x-x------------xxxx --x-------------------x-x-x-x-x-x-------x-x-x-x-x-x-------x-x-x-x-x-x ---------x---x-x-x---x---x-x-x---xxxxx---x---x---x-x-x---x---x-x-xxxxx x---------------------------------------------------------------------x -----------------------x-x-x-x-x-xxx-xxx-x-x-x-x-x-x-x-x---x-x-x-xxx-xxx x-----------------------------------------------------------------------x -x----------------------------------xx--xx--------------------------xx--xx --------------x---x---x-x-x---x-x-x-x-x---x-x-x-x-x---x-x-x-x-x---x-x-x-x-x ---x-----------------x--------------xxxxxxxx---------x-x-x-x--------xxxxxxxx ------x---x-----x-----x---x-x-----x-x---------x-----x---x-x-----x-x---x-----x -----x-----------x-------x-x-x-x-x-x-xxxxxxxxx-x-x-x-x-x-x-x-x-x-x-x-xxxxxxxxx x-----------------------------------------------------------------------------x ---------------x---x---------------x-xxx-x-x-xxx---x---x-x-x-x-x---x-xxx-x-x-xxx SUM(A057427(a(k)): 1<=k<=n) = A005127(n). - Reinhard Zumkeller, Jul 04 2009 LINKS FORMULA T(n,k) = S(n,k) mod n, where S(n,k) = Stirling numbers of the first kind. EXAMPLE Triangle starts: 0; 1, 1; 2, 0, 1; 2, 3, 2, 1; 4, 0, 0, 0, 1; 0, 4, 3, 1, 3, 1; 6, 0, 0, 0, 0, 0, 1; .... PROG (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(stirling(n, k, 1) % n, ", "); ); print(); ); } \\ Michel Marcus, Aug 10 2015 CROSSREFS Cf. A000040, A008275, A061006 (first column). Sequence in context: A079686 A005813 A049262 * A323671 A284265 A119464 Adjacent sequences:  A145198 A145199 A145200 * A145202 A145203 A145204 KEYWORD nonn,tabl AUTHOR Tilman Neumann, Oct 04 2008, Oct 06 2008 STATUS approved

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Last modified September 25 05:51 EDT 2020. Contains 337335 sequences. (Running on oeis4.)