The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A158902

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A158902

Triangle read by rows: the matrix product A051731 * A158821.
(history; published version)

#16 by Alois P. Heinz at Wed Feb 01 07:06:49 EST 2023

STATUS

reviewed

approved

#15 by Michel Marcus at Wed Feb 01 06:17:12 EST 2023

STATUS

proposed

reviewed

#14 by Jean-François Alcover at Wed Feb 01 04:41:42 EST 2023

STATUS

editing

proposed

#13 by Jean-François Alcover at Wed Feb 01 04:41:33 EST 2023

MATHEMATICA

m = 12; (* number of rows *)

T1[n_, k_] := Boole[Mod[n, k] == 0];

T2[n_, k_] := Which[n == k, 1, k == 1, n-1, True, 0];

T = Array[T1, {m, m}].Array[T2, {m, m}];

Table[T[[n, k]], {n, m}, {k, n}] // Flatten (* Jean-François Alcover, Feb 01 2023 *)

STATUS

approved

editing

#12 by N. J. A. Sloane at Thu Jan 08 17:28:48 EST 2015

STATUS

editing

approved

#11 by N. J. A. Sloane at Thu Jan 08 17:28:33 EST 2015

EXTENSIONS

Wrong A-number in definition corrected by _Michel Marcus_, Robert Israel_, Jan 08 2015

STATUS

reviewed

editing

#10 by R. J. Mathar at Thu Jan 08 15:28:55 EST 2015

STATUS

proposed

reviewed

Discussion

Thu Jan 08

16:41

Robert Israel: I don't understand the "A-number corrected by Michel ...".  The A-number for this sequence is the same as it always was.  Correcting references to A158221 was in fact done by me.

#9 by R. J. Mathar at Thu Jan 08 15:28:36 EST 2015

STATUS

editing

proposed

#8 by R. J. Mathar at Thu Jan 08 15:28:20 EST 2015

NAME

Triangle read by rows, : the matrix product A051731 * A158821.

COMMENTS

Row sums = sigma(n), A000203: (1, 3, 4, 7, 6, 12, 8,...). Left border = A158901: (1, 2, 3, 5, 5, 9, 7,...).

FORMULA

Triangle read by rows, A051731 * A158821; where A051731 = the inverse Mobius transform and A158821 = an infinite lower triangular matrix with (1, 1, 2, 3, 4, 5,...) as the left border and (1, 1, 1,...) as the right border.

T(n,n) = 1.

T(n,1) = A158901(n).

MAPLE

A158902 := proc(n, k)

add( A051731(n, j)*A158821(j-1, k-1), j=k..n) ;

end proc:

seq(seq(A158902(n, k), k=1..n), n=1..12) ; # R. J. Mathar, Jan 08 2015

CROSSREFS

Cf. A158821, A051731, A158901, A000203 (row sums).

AUTHOR

Gary W. Adamson & _and _Mats Granvik_, Mar 29 2009

EXTENSIONS

A-number corrected by Michel Marcus, Jan 08 2015

STATUS

proposed

editing

#7 by Michel Marcus at Thu Jan 08 14:32:11 EST 2015

STATUS

editing

proposed