The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A323345 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A323345

Square array read by ascending antidiagonals: T(n, k) is the number of partitions of n where parts, if sorted in ascending order, form an arithmetic progression (AP) with common difference of k; n >= 1, k >= 0.
(history; published version)

#23 by Vaclav Kotesovec at Mon Oct 21 06:33:40 EDT 2024

STATUS

editing

approved

#22 by Vaclav Kotesovec at Mon Oct 21 06:33:33 EDT 2024

CROSSREFS

Cf. A000005, A001227, A038548, A117277, A334461, A334541, A334948.

STATUS

approved

editing

#21 by N. J. A. Sloane at Mon Nov 30 08:54:53 EST 2020

STATUS

proposed

approved

#20 by Jean-François Alcover at Mon Nov 30 03:04:01 EST 2020

STATUS

editing

proposed

#19 by Jean-François Alcover at Mon Nov 30 03:03:55 EST 2020

MATHEMATICA

(* Second program: *)

nmax = 14;

col[k_] := col[k] = CoefficientList[Sum[x^(n(k n - k + 2)/2 - 1)/(1 - x^n), {n, 1, nmax}] + O[x]^nmax, x];

T[n_, k_] := col[k][[n]];

Table[T[n-k, k], {n, 1, nmax}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Nov 30 2020 *)

STATUS

approved

editing

#18 by Bruno Berselli at Tue May 05 11:48:20 EDT 2020

STATUS

reviewed

approved

#17 by Hugo Pfoertner at Tue May 05 10:58:12 EDT 2020

STATUS

proposed

reviewed

#16 by Joerg Arndt at Tue May 05 10:36:52 EDT 2020

STATUS

editing

proposed

#15 by Joerg Arndt at Tue May 05 10:36:45 EDT 2020

FORMULA

The g.f. for column d is Sum_{k>=1} x^(k*(d*k-d+2)/2)/(1-x^k) [information taken from A117277]. - Joerg Arndt, May 05 2020

STATUS

approved

editing

#14 by Joerg Arndt at Thu Jan 24 02:02:21 EST 2019

STATUS

reviewed

approved