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A122793 Connell sum sequence (partial sums of the Connell sequence). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)

LINKS

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.

FORMULA

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)