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A122793 Connell sum sequence (partial sums of the Connell sequence). 7


%S 1,3,7,12,19,28,38,50,64,80,97,116,137,160,185,211,239,269,301,335,

%T 371,408,447,488,531,576,623,672,722,774,828,884,942,1002,1064,1128,

%U 1193,1260,1329,1400,1473,1548,1625,1704,1785,1867,1951,2037,2125,2215,2307,2401,2497,2595,2695,2796,2899,3004,3111,3220

%N Connell sum sequence (partial sums of the Connell sequence).

%C 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).

%C a(n) is a sharp upper bound for the value of a gamma-labeling of a graph with n edges. (cf. Bullington)

%H Grady D. Bullington, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Bullington/bullington7.html">The Connell Sum Sequence</a>, J. Integer Seq. 10 (2007), Article 07.2.6. (includes direct formula for a(n))

%H Ian Connell, <a href="http://www.jstor.org/stable/2309358">Elementary Problem E1382</a>, American Mathematical Monthly, v. 66, no. 8 (October, 1959), p. 724.

%H Douglas E. Iannucci and Donna Mills-Taylor, <a href="http://www.cs.uwaterloo.ca/journals/JIS/IANN/iann1.html">On Generalizing the Connell Sequence</a>, J. Integer Sequences, Vol. 2, 1999, #99.1.7.

%F a(n) = (n-th triangular number)-n+(n-th partial sum of A122797).

%F 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

%Y Cf. A001614, A045928, A045929, A045930.

%Y Cf. A122794, A122795, A122796, A122797, A122798, A122799, A122800.

%K nonn,easy

%O 1,2

%A Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)