This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081490 #24 Oct 18 2022 15:01:48
%S A081490 1,2,4,9,19,36,62,99,149,214,296,397,519,664,834,1031,1257,1514,1804,
%T A081490 2129,2491,2892,3334,3819,4349,4926,5552,6229,6959,7744,8586,9487,
%U A081490 10449,11474,12564,13721,14947,16244,17614,19059,20581,22182,23864,25629
%N A081490 Leading term of n-th row of A081491.
%C A081490 First differences are given by A002522 = n^2 + 1. Second differences are odd numbers given by A005408.
%C A081490 a(1)=1, a(2)=2, (a(n+1) -a(n)) - (a(n) -a(n-1)) = 2*(n-1)-1. - _Ben Paul Thurston_, Aug 22 2009
%H A081490 G. C. Greubel, <a href="/A081490/b081490.txt">Table of n, a(n) for n = 1..1000</a>
%H A081490 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081490 a(1) = 1, a(n) = A081489(n-1) + 1.
%F A081490 From _R. J. Mathar_, Feb 06 2010: (Start)
%F A081490 G..f: x*(1-2*x+2*x^2+x^3)/(x-1)^4.
%F A081490 a(n) = n*(2*n^2 -9*n +19)/6 -1. (End)
%F A081490 a(n) = (n-2)^2 + a(n-1)+1, n>1. - _Gary Detlefs_, Jun 29 2010
%F A081490 a(1)=1, a(2)=2, a(3)=4, a(4)=9, a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Harvey P. Dale_, Apr 30 2011
%p A081490 with (combinat):a:=n->sum(fibonacci(3,i), i=0..n):seq(a(n)+1, n=-1..42); # _Zerinvary Lajos_, Apr 25 2008
%t A081490 Rest[CoefficientList[Series[x (1-2x+2x^2+x^3)/(x-1)^4,{x,0,50}],x]] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,2,4,9}, 50] (* _Harvey P. Dale_, Apr 30 2011 *)
%o A081490 (PARI) vector(50, n, (2*n^3-9*n^2+19*n-6)/6) \\ _G. C. Greubel_, Aug 13 2019
%o A081490 (Magma) [(2*n^3-9*n^2+19*n-6)/6: n in [1..50]]; // _G. C. Greubel_, Aug 13 2019
%o A081490 (Sage) [(2*n^3-9*n^2+19*n-6)/6 for n in (1..50)] # _G. C. Greubel_, Aug 13 2019
%o A081490 (GAP) List([1..50], n-> (2*n^3-9*n^2+19*n-6)/6); # _G. C. Greubel_, Aug 13 2019
%Y A081490 Cf. A002522, A005408, A081489, A081491, A081492.
%K A081490 nonn,easy
%O A081490 1,2
%A A081490 _Amarnath Murthy_, Mar 25 2003
%E A081490 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003