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A152947
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a(n) = 1 + (n-2)*(n-1)/2.
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26
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1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379
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OFFSET
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1,3
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COMMENTS
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The sequence is the sum of upward sloping terms in an infinite lower triangle with 1's in the leftmost column and the odd integers in all other columns. - Gary W. Adamson, Jan 29 2014
For n > 1, if Kruskal's algorithm is run on a weighted connected graph of n nodes, then a(n) is the maximum number of iterations required to reach a spanning tree. - Eric M. Schmidt, Jun 04 2016
It can be observed that A152947/A000079, whose reduced numerators are A213671, is identical to its inverse binomial transform (except for signs); this shows that it is an "autosequence" (more precisely, an autosequence of the second kind). - Jean-François Alcover (this remark is due to Paul Curtz), Jun 20 2016
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LINKS
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FORMULA
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E.g.f.: (4 - 2*x + x^2)*exp(x)/2 - 2.
Sum_{n>=1} 1/a(n) = 2*Pi*tanh(sqrt(7)*Pi/2)/sqrt(7) + 1 = A226985 + 1. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [1+binomial(n, 2) for n in range(0, 54)] # Zerinvary Lajos, Mar 12 2009
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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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STATUS
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approved
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