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A034262
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a(n) = n^3 + n.
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36
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0, 2, 10, 30, 68, 130, 222, 350, 520, 738, 1010, 1342, 1740, 2210, 2758, 3390, 4112, 4930, 5850, 6878, 8020, 9282, 10670, 12190, 13848, 15650, 17602, 19710, 21980, 24418, 27030, 29822, 32800, 35970, 39338, 42910, 46692, 50690, 54910
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OFFSET
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0,2
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COMMENTS
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After 0, sum of next n even numbers:
... 2, 2
... 4, 6, 10
... 8, 10, 12, 30
.. 14, 16, 18, 20, 68
.. 22, 24, 26, 28, 30, 130
.. 32, 34, 36, 38, 40, 42, 222 etc. (End)
Sequence occurs in the binomial identity Sum_{k = 0..n} a(k)* binomial(n,k)/binomial(n+k,k) = n*(n + 1)/2. Cf. A092181 and A155977. - Peter Bala, Feb 12 2019
For n >= 2, a(n) is the sum of the numbers in the 1st and last columns of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 17 2021
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LINKS
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FORMULA
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For n>1, a(n) = floor(n^5/(n^2-1)). - Gary Detlefs, Feb 10 2010
Sum_{n>=1} 1/a(n) = 0.6718659855... = gamma + Re psi(1+i) = A001620+A248177. [Borwein et al., J. Math. Anal. Appl. 316 (2006) 328]. - R. J. Mathar, Jul 17 2012
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MATHEMATICA
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 21 2000
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STATUS
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approved
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