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A008514
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4-dimensional centered cube numbers.
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7
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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a(n) = n^4 + (n+1)^4.
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.: (1+10*x+x^2)*(1+x)^2/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 09 2009
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), with a(0) = 1, a(1) = 17, a(2) = 97, a(3) = 337, a(4) = 881. - Harvey P. Dale, Jan 28 2013
a(n) = 4*(n+n^2) + 2*(n+n^2)^2 + 1. - Avi Friedlich, Mar 31 2015
a(n) = 2*A002061(n+1)^2 - 1. - Bruce J. Nicholson, Apr 14 2017
a(n) = A047838(2*(n^2+n+1)). - David James Sycamore, Aug 01 2018
E.g.f.: (1 + 16*x + 32*x^2 + 16*x^3 + 2*x^4)*exp(x). - G. C. Greubel, Nov 09 2019
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MAPLE
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seq(n^4+(n+1)^4, n=0..40);
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MATHEMATICA
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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 *)
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PROG
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(Sage) [i^4+(i+1)^4 for i in range(0, 36)] # Zerinvary Lajos, Jul 03 2008
(MAGMA) [(n+1)^4+n^4: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011
(PARI) a(n) = n^4 + (n+1)^4; \\ Altug Alkan, Aug 01 2018
(GAP) List([0..30], n->n^4+(n+1)^4); # Muniru A Asiru, Aug 02 2018
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CROSSREFS
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Cf. A002061, A047838, A152913.
Sequence in context: A078902 A103766 A165347 * A152913 A184327 A331877
Adjacent sequences: A008511 A008512 A008513 * A008515 A008516 A008517
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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