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A152773
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3 times heptagonal numbers: a(n) = 3n(5n-3)/2.
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16
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0, 3, 21, 54, 102, 165, 243, 336, 444, 567, 705, 858, 1026, 1209, 1407, 1620, 1848, 2091, 2349, 2622, 2910, 3213, 3531, 3864, 4212, 4575, 4953, 5346, 5754, 6177, 6615, 7068, 7536, 8019, 8517, 9030, 9558, 10101, 10659, 11232, 11820
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OFFSET
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0,2
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COMMENTS
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Also the number of 6-cycles in the (n+5)-triangular honeycomb acute knight graph. - Eric W. Weisstein, Jun 25 2017
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LINKS
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FORMULA
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a(n) = (15n^2 - 9n)/2 = A000566(n)*3.
a(0)=0, a(1)=3, a(2)=21, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, May 08 2012
Sum_{n>=1} 1/a(n) = tan(Pi/10)*Pi/9 - sqrt(5)*log(phi)/9 + 5*log(5)/18, where phi is the golden ratio (A001622). - Amiram Eldar, May 20 2023
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 3, 21}, 50] (* Harvey P. Dale, May 08 2012 *)
CoefficientList[Series[-((3 x^5 (1 + 4 x))/(-1 + x)^3), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 25 2017 *)
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PROG
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CROSSREFS
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Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=15: see Comments lines of A226492.
Cf. A002378 (3-cycles in triangular honeycomb acute knight graph), A045943 (4-cycles), A028896 (5-cycles).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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