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A226491
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a(n) = n*(21*n-17)/2.
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4
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0, 2, 25, 69, 134, 220, 327, 455, 604, 774, 965, 1177, 1410, 1664, 1939, 2235, 2552, 2890, 3249, 3629, 4030, 4452, 4895, 5359, 5844, 6350, 6877, 7425, 7994, 8584, 9195, 9827, 10480, 11154, 11849, 12565, 13302, 14060, 14839, 15639, 16460, 17302, 18165, 19049
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OFFSET
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0,2
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COMMENTS
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Sum of n-th dodecagonal number and n-th tridecagonal number.
Sum of reciprocals of a(n), for n>0: 0.58517199913243139233033474262449...
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LINKS
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FORMULA
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G.f.: x*(2+19*x)/(1-x)^3.
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MATHEMATICA
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Table[n (21 n - 17)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 19 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{3, -3, 1}, {0, 2, 25}, 50] (* Harvey P. Dale, Feb 01 2023 *)
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PROG
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(Magma) [n*(21*n-17)/2: n in [0..50]];
(Magma) I:=[0, 2, 25]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013
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CROSSREFS
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Cf. numbers of the form n*(n*k-k+4))/2, this sequence is the case k=21: see list in A226488.
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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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