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 A090197 #51 Nov 24 2024 02:45:39
%S A090197 1,14,45,100,185,306,469,680,945,1270,1661,2124,2665,3290,4005,4816,
%T A090197 5729,6750,7885,9140,10521,12034,13685,15480,17425,19526,21789,24220,
%U A090197 26825,29610,32581,35744,39105,42670,46445,50436,54649,59090,63765
%N A090197 a(n) = n^3 + 6*n^2 + 6*n + 1.
%C A090197 N(4,n) where N(4,x) is the 4th Narayana polynomial.
%C A090197 Number of corona of a triangle of order n surrounded by triangles of order n. - _Craig Knecht_, Oct 30 2024
%H A090197 Vincenzo Librandi, <a href="/A090197/b090197.txt">Table of n, a(n) for n = 0..1000</a>
%H A090197 Craig Knecht, <a href="/A090197/a090197_1.png">Area of the coronal frames of T2</a>.
%H A090197 Craig Knecht, <a href="/A090197/a090197.png">Corona of a triangle of order n</a>.
%H A090197 Craig Knecht, <a href="/A090197/a090197.gif">100 frame animation for n=4 triangle surrounding itself</a>.
%H A090197 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A090197 a(n) = N(4,n) = Sum_{k>0} A001263(4, k)*n^(k-1) = (n+1)*(n^2+5*n+1).
%F A090197 G.f.: (1 + 10*x - 5*x^2) / (x-1)^4. - _R. J. Mathar_, Sep 07 2011
%F A090197 a(n) + A016921(n+1) = (n+2)^3. - _Bruno Berselli_, Jun 24 2012
%F A090197 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 24 2012
%F A090197 E.g.f.: exp(x)*(1 + 13*x + 9*x^2 + x^3). - _Stefano Spezia_, Nov 22 2024
%t A090197 LinearRecurrence[{4,-6, 4, -1},{1,14,45,100},40] (* _Vincenzo Librandi_, Jun 24 2012 *)
%o A090197 (PARI) n^3+6*n^2+6*n+1 \\ _Charles R Greathouse IV_, Jan 17 2012
%o A090197 (Magma) I:=[1, 14, 45, 100]; [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..50]]; // _Vincenzo Librandi_, Jun 24 2012
%Y A090197 For N(3,n), see A028387.
%Y A090197 Cf. A001263, A016921.
%K A090197 nonn,easy
%O A090197 0,2
%A A090197 _Philippe Deléham_, Jan 22 2004