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 A100504 a(n) = (4*n^3 + 6*n^2 + 8*n + 6)/3. 3
 2, 8, 26, 64, 130, 232, 378, 576, 834, 1160, 1562, 2048, 2626, 3304, 4090, 4992, 6018, 7176, 8474, 9920, 11522, 13288, 15226, 17344, 19650, 22152, 24858, 27776, 30914, 34280, 37882, 41728, 45826, 50184, 54810, 59712, 64898, 70376, 76154, 82240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Bisection of A000125. This sequence is related to A002061 by a(n) = (n+1)*A002061(n+1) + Sum_{i=0..n} A002061(i). - Bruno Berselli, Dec 19 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = a(n-1) + (2*n)^2 + 2. - Philippe Deléham, Jan 18 2012 From Vincenzo Librandi, Jun 26 2012: (Start) G.f.: 2*(1+3*x^2)/(1-x)^4; a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) From G. C. Greubel, Apr 03 2023: (Start) a(n) = 2 + 2*A037237(n-1). E.g.f.: (2/3)*(3 + 9*x + 9*x^2 + 2*x^3)*exp(x). (End) MATHEMATICA CoefficientList[Series[2*(1+3x^2)/((1-x)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2012 *) LinearRecurrence[{4, -6, 4, -1}, {2, 8, 26, 64}, 40] (* Harvey P. Dale, Dec 27 2015 *) PROG (PARI) a(n)=n*(4*n^2+6*n+8)/3+2 \\ Charles R Greathouse IV, Jan 18 2012 (Magma) I:=[2, 8, 26, 64]; [n le 4 select I[n] else 4*Self(n-1) -6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 26 2012 (SageMath) [2 + 2*n*(2*n^2+3*n+4)/3 for n in range(41)] # G. C. Greubel, Apr 03 2023 CROSSREFS Cf. A037237. Sequence in context: A212527 A227015 A216929 * A327600 A099416 A211885 Adjacent sequences: A100501 A100502 A100503 * A100505 A100506 A100507 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 24 2004 EXTENSIONS More terms from Hugo Pfoertner, Nov 25 2004 New name based on formula from Ralf Stephan STATUS approved

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Last modified June 9 08:15 EDT 2023. Contains 363168 sequences. (Running on oeis4.)