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A163761
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a(n) = 10*n*(n+1).
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3
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0, 20, 60, 120, 200, 300, 420, 560, 720, 900, 1100, 1320, 1560, 1820, 2100, 2400, 2720, 3060, 3420, 3800, 4200, 4620, 5060, 5520, 6000, 6500, 7020, 7560, 8120, 8700, 9300, 9920, 10560, 11220, 11900, 12600, 13320, 14060, 14820, 15600, 16400, 17220, 18060, 18920
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OFFSET
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0,2
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COMMENTS
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20 times the n-th triangular number.
a(n) is the number of one-sided n-step prudent walks, from (0,0) to (3,3), for n-6 is even. - Shanzhen Gao, Apr 26 2011
Numbers k such that 10*k + 25 is a square. - Bruno Berselli, May 14 2018
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LINKS
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FORMULA
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G.f.: 20*x/(1-x)^3.
Sum_{n>=1} 1/a(n) = 1/10.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/10.
Product_{n>=1} (1 - 1/a(n)) = -(10/Pi)*cos(sqrt(7/5)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (10/Pi)*cos(sqrt(3/5)*Pi/2). (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 20, 60}, 50] (* or *) Table[10*n*(n+1), {n, 0, 50}] (* G. C. Greubel, Aug 03 2017 *)
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PROG
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(Magma) [10*n*(n+1): n in [0..50]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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