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Revision History for A080260

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A080260
a(n)=1+(1/12)(n*(n+1)*(n+3)*(4-n)).
(history; published version)
#9 by Ray Chandler at Fri Jul 31 12:23:10 EDT 2015
STATUS

editing

approved

#8 by Ray Chandler at Fri Jul 31 12:23:08 EDT 2015
LINKS

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

STATUS

approved

editing

#7 by Harvey P. Dale at Sat Sep 20 16:08:10 EDT 2014
STATUS

editing

approved

#6 by Harvey P. Dale at Sat Sep 20 16:07:58 EDT 2014
FORMULA

a(0)=1, a(1)=3, a(2)=6, a(3)=7, a(4)=1, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Sep 20 2014

MATHEMATICA

Table[1+(n(n+1)(n+3)(4-n))/12, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 3, 6, 7, 1}, 50] (* Harvey P. Dale, Sep 20 2014 *)

STATUS

approved

editing

#5 by Joerg Arndt at Tue Jul 16 08:08:24 EDT 2013
STATUS

proposed

approved

#4 by Michel Marcus at Tue Jul 16 07:51:55 EDT 2013
STATUS

editing

proposed

#3 by Michel Marcus at Tue Jul 16 06:35:51 EDT 2013
NAME

a(n)=1+(1/12)(n*(n-+1)*(n+3)*(4-n)).

FORMULA

a(n) = A002378(n) - A002415(n) + 1.

PROG

(PARI) a(n) = 1+(1/12)*(n*(n+1)*(n+3)*(4-n)) \\ Michel Marcus, Jul 16 2013

EXTENSIONS

Definition corrected by Michel Marcus, Jul 16 2013

Discussion
Tue Jul 16
07:51
Michel Marcus: Typo found.
Bit rusty.
#2 by Michel Marcus at Tue Jul 16 05:46:50 EDT 2013
FORMULA

G.f.: (1 - 2x + x^2 - 3x^3 + x^4)/(1 - x)^5 a(n)=A002378(n)-A002415(n)+1.

a(n)=A002378(n)-A002415(n)+1.

STATUS

approved

editing

Discussion
Tue Jul 16
05:50
Michel Marcus: Problem : definition does not give terms
But formula does.
05:50
Michel Marcus: (11:48) gp >1+(1/12)*(n*(n-1)*(n+3)*(4-n))
%1460 = -1/12*n^4 + 1/6*n^3 + 11/12*n^2 - n + 1
(11:49) gp >n*(n+1) - n^2*(n^2-1)/12 + 1
%1461 = -1/12*n^4 + 13/12*n^2 + n + 1
05:52
Michel Marcus: Going to write to Mario.
06:03
Michel Marcus: Undelivered Mail Returned to Sender:
User Unknown in domain
06:04
Michel Marcus: I think there is atypo in definition.
#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
NAME

a(n)=1+(1/12)(n*(n-1)*(n+3)*(4-n)).

DATA

1, 3, 6, 7, 1, -19, -62, -139, -263, -449, -714, -1077, -1559, -2183, -2974, -3959, -5167, -6629, -8378, -10449, -12879, -15707, -18974, -22723, -26999, -31849, -37322, -43469, -50343, -57999, -66494, -75887, -86239, -97613, -110074, -123689, -138527, -154659, -172158, -191099, -211559

OFFSET

0,2

COMMENTS

a(n) is the determinant of the n X n matrix M with m(i,i)=2i+1, m(i,j)=i+j.

FORMULA

G.f.: (1 - 2x + x^2 - 3x^3 + x^4)/(1 - x)^5 a(n)=A002378(n)-A002415(n)+1

KEYWORD

easy,sign

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Feb 11 2003

STATUS

approved

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