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 A003777 a(n) = n^3 + n^2 - 1. 5
 1, 11, 35, 79, 149, 251, 391, 575, 809, 1099, 1451, 1871, 2365, 2939, 3599, 4351, 5201, 6155, 7219, 8399, 9701, 11131, 12695, 14399, 16249, 18251, 20411, 22735, 25229, 27899, 30751, 33791, 37025, 40459, 44099, 47951, 52021, 56315, 60839, 65599, 70601, 75851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence in related to A095794 by a(n) = n*A095794(n) - Sum_{i=1..n-1} A095794(i), for n > 1. - Bruno Berselli, Dec 28 2010 a(n) is the area of a triangle with vertices at points (n-1,(n-1)^2), (n,n^2), and ((n+1)^2,n+1). - J. M. Bergot, Jun 03 2014 Old name was: "Number of stacks of n pikelets, distance 3 flips from a well-ordered stack". LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(1+7*x-3*x^2+x^3)/(1-x)^4. Also, a(n) = 2*A002411(n) - 1 = A000578(n-1) + A001107(n). - Bruno Berselli, Dec 28 2010 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. - Wesley Ivan Hurt, Oct 08 2017 MAPLE A003777:=n->n^3+n^2-1; seq(A003777(n), n=1..50); # Wesley Ivan Hurt, Jun 04 2014 MATHEMATICA Table[n^3+n^2-1, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *) CoefficientList[Series[(1 + 7 x - 3 x^2 + x^3) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 20 2013 *) PROG (Magma) [(n^3+n^2-1): n in [1..50]]; // Vincenzo Librandi, Apr 06 2011 (PARI) a(n)=n^3+n^2-1 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000578, A001107, A002411, A095794. Sequence in context: A233546 A092069 A103115 * A222512 A297539 A323691 Adjacent sequences: A003774 A003775 A003776 * A003778 A003779 A003780 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jun 14 1998 EXTENSIONS More terms from Wesley Ivan Hurt, Jun 04 2014 Entry revised by N. J. A. Sloane, Jun 15 2014 STATUS approved

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Last modified November 26 20:27 EST 2022. Contains 358362 sequences. (Running on oeis4.)