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A055580
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Björner-Welker sequence: 2^n*(n^2 + n + 2) - 1.
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15
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1, 7, 31, 111, 351, 1023, 2815, 7423, 18943, 47103, 114687, 274431, 647167, 1507327, 3473407, 7929855, 17956863, 40370175, 90177535, 200278015, 442499071, 973078527, 2130706431, 4647288831, 10099884031, 21877489663
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OFFSET
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0,2
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COMMENTS
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a(n) is the d=1 Betti number of the complement of '3-equal' arrangements in n-dimensional real space, see Björner-Welker reference, Table I, pp. 308-309, column '1' with k=3 and Th. 5.2, pp. 297-298.
Binomial transform of [1/2, 2/3, 3/4, 4/5, ...] = 1/2, 7/6, 31/12, 111/20, 351/30, 1023/42, ..., where 2, 6, 12, 20, ... = A002378 (deleting the zero). - Gary W. Adamson, Apr 28 2005
Number of three-dimensional block structures associated with n joint systems in the construction of stable underground structures. - Richard M. Green, Jul 26 2011
Number of monotone mappings from the chain with three points to the complete binary tree of height n (n+1 levels). For example, the seven monotone mappings from the chain with three points (denoted 1,2,3, in order) to the complete binary tree with two levels (with a the root of the tree, and b, c the atoms) are: f(1)=f(2)=f(3)=a; f(1)=f(2)=a, f(3)=b; f(1)=f(2)=a, f(3)=c; f(1)=a, f(2)=f(3)=b; f(1)=a, f(2)=f(3)=c; f(1)=f(2)=f(3)=b; f(1)=f(2)=f(3)=c. - Pietro Codara, Mar 26 2015
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REFERENCES
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H. Barcelo and S. Smith, The discrete fundamental group of the order complex of B_n, Abstract 1020-05-141, 1020th Meeting Amer. Math. Soc., Cincinatti, Ohio, Oct 21-22, 2006.
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n-1} a(j) + A045618(n), n >= 1.
G.f.: 1/((1-2*x)^3*(1-x)).
E.g.f.: 2*(1 + 2*x + 2*x^2)*exp(2*x) - exp(x). - G. C. Greubel, Oct 28 2016
a(n) = Sum_{k=0..n+1} Sum_{i=0..n+1} i^2 * C(k,i). - Wesley Ivan Hurt, Sep 21 2017
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MATHEMATICA
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LinearRecurrence[{7, -18, 20, -8}, {1, 7, 31, 111}, 30] (* Harvey P. Dale, Nov 27 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Edited (for consistency with change of offset) by M. F. Hasler, Nov 03 2012
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STATUS
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approved
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