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Search: id:A124647
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| 1, 9, 45, 189, 729, 2673, 9477, 32805, 111537, 373977, 1240029, 4074381, 13286025, 43046721, 138706101, 444816117, 1420541793, 4519905705, 14334558093, 45328197213, 142958160441, 449795187729, 1412147682405, 4424729404869
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OFFSET
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0,2
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COMMENT
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1 - 1/9 + 1/45 - 1/189 +...= Pi/(2*sqrt(3))
If X_1,X_2,...,X_n are 3-blocks of a (4n+1)-set X then, for n>=1, a(n) is the number of (n+1)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 50
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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G.f.: (1+3*x)/(1-3*x)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 07 2009]
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009: (Start)
a(n) = 6*a(n-1)-9*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
a(n) = 9*A081038(n-1) for n > 0. (End)
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EXAMPLE
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a(3) = 189 = 7*(3^3)
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PROGRAM
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(MAGMA) [ (2*n+1)*3^n: n in [0..23] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009]
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CROSSREFS
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Sequence in context: A036826 A022574 A050574 this_sequence A111640 A024209 A026092
Adjacent sequences: A124644 A124645 A124646 this_sequence A124648 A124649 A124650
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 22 2006
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009
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