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A206399
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a(0) = 1; for n>0, a(n) = 41*n^2 + 2.
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35
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1, 43, 166, 371, 658, 1027, 1478, 2011, 2626, 3323, 4102, 4963, 5906, 6931, 8038, 9227, 10498, 11851, 13286, 14803, 16402, 18083, 19846, 21691, 23618, 25627, 27718, 29891, 32146, 34483, 36902, 39403, 41986, 44651, 47398, 50227, 53138, 56131, 59206, 62363
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OFFSET
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0,2
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COMMENTS
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Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=3, s=4. After 1, all terms are in A000408.
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LINKS
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FORMULA
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O.g.f.: (1 + x)*(1 + 39*x + x^2)/(1 - x)^3.
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MATHEMATICA
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Join[{1}, 41 Range[39]^2 + 2]
CoefficientList[Series[(1 + x) (1 + 39 x + x^2) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 18 2013 *)
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PROG
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(Magma) [n eq 0 select 1 else 41*n^2+2: n in [0..39]];
(Magma) I:=[1, 43, 166, 371]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..41]]; // Vincenzo Librandi, Aug 18 2013
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CROSSREFS
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Sequences of the same type: A005893, A005897, A005899, A005901, A005903, A005905, A005914, A005918, A005919, A008527, A010000-A010023.
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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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