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 A206399 a(0) = 1; for n>0, a(n) = 41*n^2 + 2. 35
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA O.g.f.: (1 + x)*(1 + 39*x + x^2)/(1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. - Wesley Ivan Hurt, Dec 18 2020 MATHEMATICA 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 *) PROG (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 (PARI) a(n)=if(n, 41*n^2+2, 1) \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Sequences of the same type: A005893, A005897, A005899, A005901, A005903, A005905, A005914, A005918, A005919, A008527, A010000-A010023. Sequence in context: A235392 A078852 A078956 * A123040 A142016 A140640 Adjacent sequences:  A206396 A206397 A206398 * A206400 A206401 A206402 KEYWORD nonn,easy AUTHOR Bruno Berselli, Feb 07 2012 STATUS approved

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Last modified January 24 19:12 EST 2021. Contains 340411 sequences. (Running on oeis4.)