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Search: id:A002940
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| A002940 |
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Arrays of dumbbells.
(Formerly M3415 N1381)
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+0
12
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| 1, 4, 11, 26, 56, 114, 223, 424, 789, 1444, 2608, 4660, 8253, 14508, 25343, 44030, 76136, 131110, 224955, 384720, 656041, 1115784, 1893216, 3205416, 5416441, 9136084, 15384563, 25866914, 43429784, 72821274, 121953943, 204002680
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Whitney transform of n. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005
a(n-1) is the permanent of the n X n 0-1 matrix with 1 in (i,j) position iff (i=1 and j<n) or 0<=i-j<=2 or (j=n and i>1). For example, with n=5, a(4) = per([[1, 1, 1, 1, 0], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [0, 1, 1, 1, 1], [0, 0, 1, 1, 1]]) = 26. - David Callan (callan(AT)stat.wisc.edu), Jun 07 2006
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
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FORMULA
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a(n)=2*a(n-1)-a(n-3)+A000045(n+1)
G.f.: (1+x)/(1-x-x^2)^2/(1-x).
a(n)=sum{k=0..n, sum{i=0..n, C(k, i-k)}*k}; - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005
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CROSSREFS
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Cf. A002941, A002889, A055608, A062123-A062127, A046741.
Cf. A001925, A054454, A006478.
Adjacent sequences: A002937 A002938 A002939 this_sequence A002941 A002942 A002943
Sequence in context: A109414 A027966 A027660 this_sequence A030196 A000295 A125128
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Jun 02 2000
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