login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059826 a(n) = (n^2 - n + 1)*(n^2 + n + 1). 17
1, 3, 21, 91, 273, 651, 1333, 2451, 4161, 6643, 10101, 14763, 20881, 28731, 38613, 50851, 65793, 83811, 105301, 130683, 160401, 194923, 234741, 280371, 332353, 391251, 457653, 532171, 615441, 708123, 810901, 924483, 1049601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Main diagonal of A082039. - Paul Barry, Apr 02 2003

The base of the natural logarithms e = 2*Sum_{n>=0} 1/(a(n)*n!) and zeta(2) = Pi^2/6 = 1 + 2*Sum_{n>=1} (-1)^(n+1)/(a(n)*n^2). - Peter Bala, Jan 20 2008

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = n^4+n^2+1. - Paul Barry, Apr 02 2003

a(n) = (n^2-n+1) * (n^2+n+1) = A002061(n) * A002061(n+1), products of two consecutive central polygonal numbers. a(n) = (n^6-1)/(n^2-1), n>1. a(n) = (n^5-n^4+n^3-n^2+n-1)/(n-1) = A062159(n)/(n-1), n>1. - Alexander Adamchuk, Apr 12 2006

O.g.f.: (-1+2*x-16*x^2-6*x^3-3*x^4) / (x-1)^5. - R. J. Mathar, Feb 26 2008

a(n) = A219069(n,1), for n > 0. - Reinhard Zumkeller, Nov 11 2012

a(n+2) = (n^2+3n+3) * (n^2+5n+7) = (t(n)+t(n+2)) * (t(n+1)+t(n+3)), where t=A000217 are triangular numbers. For n>=1, a(n+2) = t(2*t(n+2)+t(n)) -t(t(n)-1). - J. M. Bergot, Nov 29 2012

4*a(n) = (n^2+n+1)^2+(n^2-n+1)^2+(n^2+n-1)^2+(n^2-n-1)^2. [Bruno Berselli, Jul 03 2014]

a(n) = A002061(n^2). - Franklin T. Adams-Watters, Aug 01 2014

Sum_{n>=0} 1/a(n) = 1/2 + sqrt(3)*Pi*tanh(sqrt(3)*Pi/2)/6. - Amiram Eldar, Feb 14 2021

MAPLE

with(combinat): seq(fibonacci(3, n)+n^4, n=0..40); # Zerinvary Lajos, May 25 2008

MATHEMATICA

Table[n^4 + n^2 + 1, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 09 2014 *)

PROG

(PARI) { for (n=0, 1000, f=n^2 + 1; write("b059826.txt", n, " ", (f - n)*(f + n)); ) } \\ Harry J. Smith, Jun 29 2009

(Magma) [n^4+n^2+1 : n in [0..50]]; // Wesley Ivan Hurt, Jun 09 2014

CROSSREFS

Cf. A002061, A062159.

Sequence in context: A071351 A083231 A129755 * A108970 A069017 A264246

Adjacent sequences: A059823 A059824 A059825 * A059827 A059828 A059829

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 24 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 20:01 EST 2022. Contains 358362 sequences. (Running on oeis4.)