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%I #47 Jan 04 2024 08:58:58
%S 1,11,35,79,149,251,391,575,809,1099,1451,1871,2365,2939,3599,4351,
%T 5201,6155,7219,8399,9701,11131,12695,14399,16249,18251,20411,22735,
%U 25229,27899,30751,33791,37025,40459,44099,47951,52021,56315,60839,65599,70601,75851
%N a(n) = n^3 + n^2 - 1.
%C 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
%C 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
%C Old name was: "Number of stacks of n pikelets, distance 3 flips from a well-ordered stack".
%H Vincenzo Librandi, <a href="/A003777/b003777.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F 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
%F 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
%F E.g.f.: 1 + (-1 + 2*x + 4*x^2 + x^3)*exp(x). - _G. C. Greubel_, Jan 03 2024
%p A003777:=n->n^3+n^2-1; seq(A003777(n), n=1..50); # _Wesley Ivan Hurt_, Jun 04 2014
%t Table[n^3+n^2-1,{n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)
%t CoefficientList[Series[(1 + 7 x - 3 x^2 + x^3)/(1-x)^4, {x,0,50}], x] (* _Vincenzo Librandi_, Jun 20 2013 *)
%o (Magma) [(n^3+n^2-1): n in [1..50]]; // _Vincenzo Librandi_, Apr 06 2011
%o (PARI) a(n)=n^3+n^2-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (SageMath) [n^3+n^2-1 for n in range(1,51)] # _G. C. Greubel_, Jan 03 2024
%Y Cf. A000578, A001107, A002411, A028294, A028295, A095794.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jun 14 1998
%E More terms from _Wesley Ivan Hurt_, Jun 04 2014
%E Entry revised by _N. J. A. Sloane_, Jun 15 2014
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