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A046691
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a(n) = (n^2 + 5*n - 2)/2.
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17
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-1, 2, 6, 11, 17, 24, 32, 41, 51, 62, 74, 87, 101, 116, 132, 149, 167, 186, 206, 227, 249, 272, 296, 321, 347, 374, 402, 431, 461, 492, 524, 557, 591, 626, 662, 699, 737, 776, 816, 857, 899, 942, 986, 1031, 1077, 1124, 1172, 1221, 1271, 1322
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OFFSET
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0,2
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COMMENTS
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If Y_i (i=1,2,3,4) are 2-blocks of an n-set X then, for n>=8, a(n-3) is the number of (n-2)-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Nov 09 2007
Numbers m > -3 such that 8*m + 33 is a square. - Bruno Berselli, Aug 20 2015
a(n-1) yields the second Betti number of a path graph on n vertices. - Samuel J. Bevins, Nov 27 2022
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LINKS
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FORMULA
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G.f.: (-1 + 5*x - 3*x^2)/(1 - x)^3.
E.g.f.: (1/2)*(x^2 + 6*x - 2)*exp(x). - G. C. Greubel, Jul 13 2017
Sum_{n>=0} 1/a(n) = 7/12 + 2*Pi*tan(sqrt(33)*Pi/2)/sqrt(33). - Vaclav Kotesovec, Dec 31 2022
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [Binomial(n+3, 2) -4: n in [0..50]]; // G. C. Greubel, Jul 31 2022
(SageMath) [(n^2 +5*n -2)/2 for n in (0..50)] # G. C. Greubel, Jul 31 2022
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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