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Search: id:A037254
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| A037254 |
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Triangle (a(n,k), n >= 1, 1<=k<=n) of non-distorting tie-avoiding integer vote weights. |
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4
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| 1, 1, 2, 2, 3, 4, 3, 5, 6, 7, 6, 9, 11, 12, 13, 11, 17, 20, 22, 23, 24, 22, 33, 39, 42, 44, 45, 46, 42, 64, 75, 81, 84, 86, 87, 88, 84, 126, 148, 159, 165, 168, 170, 171, 172, 165, 249, 291, 313, 324, 330, 333, 335, 336, 337, 330, 495, 579, 621, 643, 654, 660, 663, 665
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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Solution to Board of Directors Problem, J. Rec. Math., 9 (No. 3, 1977), 240.
M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 122-123.
Kreweras, G.; Sur quelques problemes relatifs au vote pondere, [ Some problems of weighted voting ] Math. Sci. Humaines No. 84 (1983), 45-63.
T. V. Narayana, Lattice Path Combinatorics with Statistical Applications. Univ. Toronto Press, 1979, pp. 100-101.
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FORMULA
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a(1, 1)=1; a(n, 1)=a(n-1, [ (n+1)/2 ]); a(n, k)=a(n, 1)+a(n-1, k-1) for k>1.
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EXAMPLE
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1; 1,2; 2,3,4; 3,5,6,7; 6,9,11,12,13; ...
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CROSSREFS
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Row sums give A005254. See also A005318, A096858.
Adjacent sequences: A037251 A037252 A037253 this_sequence A037255 A037256 A037257
Sequence in context: A128282 A106408 A096858 this_sequence A071506 A125920 A078664
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from (and formula corrected by) James A. Sellers (sellersj(AT)math.psu.edu), Feb 04 2000
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