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A122793
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Connell sum sequence (partial sums of the Connell sequence).
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7
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1, 3, 7, 12, 19, 28, 38, 50, 64, 80, 97, 116, 137, 160, 185, 211, 239, 269, 301, 335, 371, 408, 447, 488, 531, 576, 623, 672, 722, 774, 828, 884, 942, 1002, 1064, 1128, 1193, 1260, 1329, 1400, 1473, 1548, 1625, 1704, 1785, 1867, 1951, 2037, 2125, 2215, 2307, 2401, 2497, 2595, 2695, 2796, 2899, 3004, 3111, 3220
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OFFSET
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1,2
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COMMENTS
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a(n) = the sum of the n highest entries in the projection of the n-th tetrahedron or tetrahedral number (e.g. a(7) = 7+6+6+5+5+5+4+4).
a(n) is a sharp upper bound for the value of a gamma-labeling of a graph with n edges. (cf. Bullington)
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LINKS
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Table of n, a(n) for n=1..60.
Grady D. Bullington, The Connell Sum Sequence, J. Integer Seq. 10 (2007), Article 07.2.6. (includes direct formula for a(n))
Ian Connell, Elementary Problem E1382, American Mathematical Monthly, v. 66, no. 8 (October, 1959), p. 724.
Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.
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FORMULA
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a(n) = (n-th triangular number)-n+(n-th partial sum of A122797).
Set R=Round(Sqrt(2*n),0), then a(n) = n^2+n-R*((6*n+1)-R^2)/6. - Gerald Hillier, Nov 29 2009
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CROSSREFS
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Cf. A001614, A045928, A045929, A045930.
Cf. A122794, A122795, A122796, A122797, A122798, A122799, A122800.
Sequence in context: A025713 A022791 A025742 * A062714 A039677 A011899
Adjacent sequences: A122790 A122791 A122792 * A122794 A122795 A122796
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KEYWORD
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nonn,easy
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AUTHOR
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Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006
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STATUS
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approved
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