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 A195319 Three times second hexagonal numbers: 3*n*(2*n+1). 5
 0, 9, 30, 63, 108, 165, 234, 315, 408, 513, 630, 759, 900, 1053, 1218, 1395, 1584, 1785, 1998, 2223, 2460, 2709, 2970, 3243, 3528, 3825, 4134, 4455, 4788, 5133, 5490, 5859, 6240, 6633, 7038, 7455, 7884, 8325, 8778, 9243, 9720, 10209, 10710, 11223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 9, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Semi-axis opposite to A094159 in the same spiral. Sum of the numbers from 2*n to 4*n. - Wesley Ivan Hurt, Nov 27 2015 From Peter M. Chema, Jan 21 2017: (Start) Also 0 together with the partial sums of A017629. Digit root is 0 together with period 3: repeat [9,3,9]. Final digits cycle a length period 10: repeat [0,9,0,3,8,5,4,5,8,3]. (End) Sequence found by reading the line from 0, in the direction 0, 9, ..., in the triangle spiral. - Hans G. Oberlack, Dec 08 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Hans G. Oberlack, Triangle spiral Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 6*n^2 + 3*n = 3*A014105(n). a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Harvey P. Dale, Oct 13 2013 G.f.: 3*x*(3+x) / (1-x)^3. - Wesley Ivan Hurt, Nov 27 2015 a(n) = A000217(3*n) + 3*A000217(n). - Bruno Berselli, Aug 31 2017 E.g.f.: 3*x*(2*x+3)*exp(x). - G. C. Greubel, Dec 07 2018 MAPLE A195319:=n->6*n^2 + 3*n: seq(A195319(n), n=0..50); # Wesley Ivan Hurt, Nov 27 2015 MATHEMATICA Table[6n^2+3n, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 30}, 50] (* Harvey P. Dale, Oct 13 2013 *) CoefficientList[Series[3 x (3 + x)/(1 - x)^3, {x, 0, 50}], x] (* Wesley Ivan Hurt, Nov 27 2015 *) PROG (MAGMA) [3*n*(2*n+1): n in [0..50]]; // Vincenzo Librandi, Sep 20 2011 (PARI) a(n)=3*n*(2*n+1) \\ Charles R Greathouse IV, Oct 16 2015 (Sage) [3*n*(2*n+1) for n in range(50)] # G. C. Greubel, Dec 07 2018 (GAP) List([0..30], n -> 3*n*(2*n+1)); # G. C. Greubel, Dec 07 2018 CROSSREFS Bisection of A045943. Cf. A000217, A001318, A014105, A094159, A017629. Sequence in context: A063150 A063161 A295867 * A073399 A225275 A005919 Adjacent sequences:  A195316 A195317 A195318 * A195320 A195321 A195322 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 17 2011 STATUS approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)