Revision History for A087958
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
|
| |
|
| A087958
|
|
a(n) is the square of the n-th partial sum minus the n-th partial sum of the squares, divided by a(n-1), for all n>=1, starting with a(0)=1, a(1)=5.
(history;
published version)
|
| |
|
|
#8 by Ray Chandler at Fri Jul 31 12:41:59 EDT 2015
| |
| |
| |
|
|
#7 by Ray Chandler at Fri Jul 31 12:41:55 EDT 2015
|
|
| LINKS
|
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -1).
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#6 by Charles R Greathouse IV at Thu Nov 21 12:48:13 EST 2013
|
|
| MATHEMATICA
|
Join[{1}, LinearRecurrence[{1, 3, -1}, {5, 2, 17}, 30]] (* From ]] (* _Harvey P. Dale, _, Jul 07 2011 *)
|
| |
|
|
Discussion
|
| Thu Nov 21
| 12:48
| OEIS Server: https://oeis.org/edit/global/2062
|
| |
| |
|
|
#5 by Russ Cox at Fri Mar 30 18:36:39 EDT 2012
|
|
| AUTHOR
|
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Sep 16 2003
|
| |
|
|
Discussion
|
| Fri Mar 30
| 18:36
| OEIS Server: https://oeis.org/edit/global/213
|
| |
| |
|
|
#4 by Harvey P. Dale at Thu Jul 07 12:45:55 EDT 2011
| |
| |
| |
|
|
#3 by Harvey P. Dale at Thu Jul 07 12:45:46 EDT 2011
|
|
| MATHEMATICA
|
Join[{1}, LinearRecurrence[{1, 3, -1}, {5, 2, 17}, 30]] (* From Harvey P. Dale, Jul 07 2011 *)
|
|
| STATUS
|
approved
proposed
|
| |
| |
|
|
#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
|
|
| KEYWORD
|
nonn,new
nonn
|
|
| AUTHOR
|
Paul D . Hanna (pauldhanna(AT)juno.com), Sep 16 2003
|
| |
| |
|
|
#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004
|
|
| NAME
|
a(n) is the square of the n-th partial sum minus the n-th partial sum of the squares, divided by a(n-1), for all n>=1, starting with a(0)=1, a(1)=5.
|
|
| DATA
|
1, 5, 2, 17, 18, 67, 104, 287, 532, 1289, 2598, 5933, 12438, 27639, 59020, 129499, 278920, 608397, 1315658, 2861929, 6200506, 13470635, 29210224, 63421623, 137581660, 298636305, 647959662, 1406286917, 3051529598, 6622430687
|
|
| OFFSET
|
0,2
|
|
| FORMULA
|
a(n) = a(n-1) + 3a(n-2) - a(n-3) for n>3; G.f.: (1+4x-6x^2+x^3)/(1-x-3x^2+x^3).
|
|
| EXAMPLE
|
a(4)=18 since ((1+5+2+17)^2 - (1^2+5^2+2^2+17^2))/17 = (25^2-217)/17 = 18.
|
|
| PROG
|
(PARI) a(0)=1; a(1)=5; for(n=2, 50, a(n)=((sum(k=0, n, a(k))^2-sum(k=0, n, a(k)^2))/a(n-1))
|
|
| CROSSREFS
|
Cf. A087640, A087955, A087956, A087957.
|
|
| KEYWORD
|
nonn
|
|
| AUTHOR
|
Paul D Hanna (pauldhanna(AT)juno.com), Sep 16 2003
|
|
| STATUS
|
approved
|
| |
| |
|
|
