The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A005407 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A005407

Number of protruded partitions of n with largest part at most 6.
(history; published version)

#26 by Russ Cox at Sun Jan 05 19:51:33 EST 2025

LINKS

R. P. Stanley, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/13-3/stanley.pdf">A Fibonacci lattice</a>, Fib. Quart., 13 (1975), 215-232.

Discussion

Sun Jan 05

19:51

OEIS Server: https://oeis.org/edit/global/3012

#25 by Russ Cox at Sun Jan 05 19:24:39 EST 2025

LINKS

R. P. Stanley, <a href="httphttps://www.fq.math.ca/Scanned/13-3/stanley.pdf">A Fibonacci lattice</a>, Fib. Quart., 13 (1975), 215-232.

Discussion

Sun Jan 05

19:24

OEIS Server: https://oeis.org/edit/global/3011

#24 by Joerg Arndt at Sat Nov 19 04:31:56 EST 2022

STATUS

reviewed

approved

#23 by Michel Marcus at Sat Nov 19 02:56:43 EST 2022

STATUS

proposed

reviewed

#22 by G. C. Greubel at Sat Nov 19 02:41:12 EST 2022

STATUS

editing

proposed

#21 by G. C. Greubel at Sat Nov 19 02:40:49 EST 2022

LINKS

G. C. Greubel, <a href="/A005407/b005407.txt">Table of n, a(n) for n = 1..1000</a>

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( -1 + (1-x)^6/(&*[1-x-x^j+x^(2*j+1): j in [1..6]]) )); // G. C. Greubel, Nov 19 2022

(SageMath)

def A005407_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( -1 + (1-x)^6/product(1-x-x^j+x^(2*j+1) for j in (1..6)) ).list()

a=A005407_list(50); a[1:] # G. C. Greubel, Nov 19 2022

STATUS

approved

editing

#20 by Michael De Vlieger at Sun Dec 26 22:09:07 EST 2021

STATUS

proposed

approved

#19 by Jon E. Schoenfield at Sun Dec 26 21:18:33 EST 2021

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Sun Dec 26 21:18:28 EST 2021

FORMULA

G.f.: (1-x)^6/Product_{i=1..6} (1-x-x^i+x^(1+2*i), i=1..6) - 1. - Emeric Deutsch, Dec 19 2004

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#17 by Alois P. Heinz at Tue Sep 05 14:51:45 EDT 2017

STATUS

editing

approved