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Search: id:A062392
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| A062392 |
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a(n)=n^4-(n-1)^4+(n-2)^4-....0^4. |
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+0
6
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| 0, 1, 15, 66, 190, 435, 861, 1540, 2556, 4005, 5995, 8646, 12090, 16471, 21945, 28680, 36856, 46665, 58311, 72010, 87990, 106491, 127765, 152076, 179700, 210925, 246051, 285390, 329266, 378015, 431985, 491536, 557040, 628881, 707455
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of edges in the join of two complete graphs of order n^2 and n, K_n^2 * K_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
a(n) is equal to the partial sums of A007588, stella octangula numbers: n(2n^2 - 1). - Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 15 2006
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REFERENCES
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T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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a(n) = n(n+1)(n^2+n-1)/2 = n^4-a(n-1) = A000583(n)-a(n) = A000217(A028387(n-1)) = A000217(n)*A028387(n-1).
a(n) = SUM[i=0..n] A007588(i). a(n) = SUM[i=0..n] n*(2*n^2 - 1). a(n) = SUM[i=0..n] (1/6)*(12*n^3-6*n), n>0. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 15 2006
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CROSSREFS
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Cf. A000538, A000583. A062393 provides the result for 5th powers, A011934 for cubes, A000217 for squares, A001057 (unsigned) for nonnegative integers, A000035 (offset) for 0th powers.
Cf. A007588.
Sequence in context: A027526 A033653 A088058 this_sequence A015876 A085474 A124893
Adjacent sequences: A062389 A062390 A062391 this_sequence A062393 A062394 A062395
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 21 2001
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