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A008514 4-dimensional centered cube numbers. 4
1, 17, 97, 337, 881, 1921, 3697, 6497, 10657, 16561, 24641, 35377, 49297, 66977, 89041, 116161, 149057, 188497, 235297, 290321, 354481, 428737, 514097, 611617, 722401, 847601, 988417, 1146097 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Summation of n^4 taken two at a time. - Al Hakanson (hawkuu(AT)gmail.com), May 27 2009

The primes in this sequence are given by A152913. - Jonathan Vos Post, Aug 17, 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

FORMULA

a(n)=2*n^4+4*n^3+6*n^2+4*n+1. - Al Hakanson (hawkuu(AT)gmail.com), May 27 2009, corrected R. J. Mathar, May 29 2009

G.f.:-(x^2+10*x+1)*(x+1)^2/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 09 2009

a(0)=1, a(1)=17, a(2)=97, a(3)=337, a(4)=881, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Jan 28 2013

MAPLE

n^4+(n+1)^4;

MATHEMATICA

Total/@Partition[Range[0, 30]^4, 2, 1] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 17, 97, 337, 881}, 30](* Harvey P. Dale, Jan 28 2013 *)

PROG

(Sage) [i^4+(i+1)^4 for i in xrange(0, 36)] # Zerinvary Lajos, Jul 03 2008

(MAGMA) [(n+1)^4+n^4: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011

CROSSREFS

Cf. A152913.

Sequence in context: A078902 A103766 A165347 * A152913 A184327 A231667

Adjacent sequences:  A008511 A008512 A008513 * A008515 A008516 A008517

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 16 13:35 EDT 2014. Contains 246817 sequences.