The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A299730 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A299730

Irregular triangle read by rows: T(n,k) is the number of partitions of 3*n having exactly k prime parts; n >= 0, 0 <= k <= floor( 3*n / 2 ).
(history; published version)

#31 by Alois P. Heinz at Mon Mar 08 08:39:49 EST 2021

STATUS

proposed

approved

#30 by Jean-François Alcover at Mon Mar 08 06:39:33 EST 2021

STATUS

editing

proposed

#29 by Jean-François Alcover at Mon Mar 08 06:39:27 EST 2021

MATHEMATICA

b[n_, i_] := b[n, i] = Expand[If[n == 0 || i == 1, 1,

Sum[b[n - i*j, i - 1]*If[PrimeQ[i], x^j, 1], {j, 0, n/i}]]];

T[n_] := CoefficientList[b[3n, 3n], x];

T /@ Range[0, 12] // Flatten (* Jean-François Alcover, Mar 08 2021, after Alois P. Heinz *)

STATUS

approved

editing

#28 by Bruno Berselli at Tue Mar 13 04:17:37 EDT 2018

STATUS

reviewed

approved

#27 by Michael B. Porter at Tue Mar 13 03:45:06 EDT 2018

STATUS

proposed

reviewed

#26 by J. Stauduhar at Mon Mar 12 10:47:58 EDT 2018

STATUS

editing

proposed

#25 by J. Stauduhar at Mon Mar 12 10:47:28 EDT 2018

NAME

Irregular triangle read by rows: T(n,k) is the number of partitions of 3*n having exactly k prime parts; m n >= 0, 0 <= k <= floor( 3*n / 2 ).

STATUS

proposed

editing

Discussion

Mon Mar 12

10:47

J. Stauduhar: Yes.  Thank you.

#24 by J. Stauduhar at Sun Mar 11 21:40:49 EDT 2018

STATUS

editing

proposed

Discussion

Mon Mar 12

03:01

Michael B. Porter: In the Name, what is m?  I'm guessing it should be n.

#23 by J. Stauduhar at Sun Mar 11 21:40:43 EDT 2018

LINKS

J. Stauduhar, <a href="/A299730/b299730.txt">Table of n, a(n) for n = 0..719</a>

STATUS

approved

editing

#22 by Alois P. Heinz at Sun Mar 11 18:09:53 EDT 2018

STATUS

proposed

approved