The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A219759

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A219759

Expansion of x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6).
(history; published version)

#30 by Hugo Pfoertner at Wed Feb 14 06:43:17 EST 2024

STATUS

reviewed

approved

#29 by Joerg Arndt at Wed Feb 14 04:27:10 EST 2024

STATUS

proposed

reviewed

#28 by Michel Marcus at Wed Feb 14 03:23:33 EST 2024

STATUS

editing

proposed

#27 by Michel Marcus at Wed Feb 14 03:23:29 EST 2024

LINKS

M. H. Albert, M. D. Atkinson and Robert Brignall, <a href="http://arxiv.org/abs/1206.3183">The enumeration of three pattern classes</a>, arXiv:1206.3183 [math.CO] (2012), p. 30.

<a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (16,-112,449,-1132,1852,-1952,1264,-448,64).

PROG

(Maxima) makelist(coeff(taylor(x^4*(2-12*x+24*x^2-8*x^3-41*x^4+57*x^5-16*x^6)/((1-x)*(1-3*x+x^2)*(1-2*x)^6), x, 0, n), x, n), n, 0, 28); [_/* _Bruno Berselli_, Nov 29 2012] */

STATUS

approved

editing

#26 by Harvey P. Dale at Wed Mar 01 08:11:22 EST 2023

STATUS

editing

approved

#25 by Harvey P. Dale at Wed Mar 01 08:11:19 EST 2023

MATHEMATICA

LinearRecurrence[{16, -112, 449, -1132, 1852, -1952, 1264, -448, 64}, {0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906}, 40] (* Harvey P. Dale, Mar 01 2023 *)

STATUS

approved

editing

#24 by Charles R Greathouse IV at Thu Sep 08 08:46:04 EDT 2022

PROG

(MAGMAMagma) I:=[0, 0, 0, 0, 2, 20, 120, 570, 2355, 8841, 30906, 102187, 323053]; [n le 11 select I[n] else 16*Self(n-1) -112*Self(n-2) + 449*Self(n-3) - 1132*Self(n-4) + 1852*Self(n-5) - 1952*Self(n-6) + 1264*Self(n-7) - 448*Self(n-8) + 64*Self(n-9): n in [1..30]]; // Vincenzo Librandi, Dec 14 2012

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#23 by R. J. Mathar at Fri Aug 19 12:16:48 EDT 2022

STATUS

editing

approved

#22 by R. J. Mathar at Fri Aug 19 12:16:37 EDT 2022

MAPLE

A219759 := proc(n)

if n <= 1 then

0;

else

2^n*(881*n^2/24-14393*n/60+137+7*n^4/24-49*n^3/8+n^5/120) -384+ 64*A001906(n+2) ;

%/64 ;

end if;

end proc:

seq(A219759(n), n=0..20) ; # R. J. Mathar, Aug 19 2022

STATUS

approved

editing

#21 by Charles R Greathouse IV at Sat Jun 13 00:54:36 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (16,-112,449,-1132,1852,-1952,1264,-448,64).

Discussion

Sat Jun 13

00:54

OEIS Server: https://oeis.org/edit/global/2439