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 A099761 #64 Jan 13 2025 12:22:34
%S A099761 0,9,64,225,576,1225,2304,3969,6400,9801,14400,20449,28224,38025,
%T A099761 50176,65025,82944,104329,129600,159201,193600,233289,278784,330625,
%U A099761 389376,455625,529984,613089,705600,808201,921600,1046529,1183744,1334025
%N A099761 a(n) = ( n*(n+2) )^2.
%C A099761 Using four consecutive triangular numbers t1, t2, t3, t4, form a 2 X 2 determinant with the first row t1 and t2 and the second row t3 and t4. Squaring the determinant gives the numbers in this sequence. - _J. M. Bergot_, May 17 2012
%C A099761 Numbers k such that sqrt(1 + sqrt(k)) is an integer. - _Jaroslav Krizek_, Jan 23 2014
%H A099761 G. C. Greubel, <a href="/A099761/b099761.txt">Table of n, a(n) for n = 0..1000</a>
%H A099761 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A099761 G.f.: x*(9 +19*x -5*x^2 +x^3)/(1-x)^5. - _R. J. Mathar_, Apr 02 2011
%F A099761 a(n) = (A005563(n))^2. - _Pedro Caceres_, Aug 04 2019
%F A099761 E.g.f.: exp(x)*x*(9 + 23*x + 10*x^2 + x^3). - _Stefano Spezia_, Aug 05 2019
%F A099761 a(n) = (determinant [T(n-1) T(n) ; T(n+1) T(n+2)])^2 where T is A000217. - _J. M. Bergot_, May 17 2012 and _Bernard Schott_, Aug 06 2019
%F A099761 From _Amiram Eldar_, Jul 13 2020: (Start)
%F A099761 Sum_{n>=1} 1/a(n) = Pi^2/12 - 11/16.
%F A099761 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/24 - 5/16. (End)
%p A099761 A099761 := proc(n) n^2*(n+2)^2 ; end proc:
%p A099761 seq(A099761(n), n=0..40) ; # _R. J. Mathar_, Apr 02 2011
%t A099761 Table[1 -2m^2 +m^4, {m,40}] (* _Artur Jasinski_, Aug 15 2007 *)
%o A099761 (PARI) vector(40, n, (n^2-1)^2) \\ _G. C. Greubel_, Sep 03 2019
%o A099761 (Magma) [(n*(n+2))^2: n in [0..40]]; // _G. C. Greubel_, Sep 03 2019
%o A099761 (Sage) [(n*(n+2))^2 for n in (0..40)] # _G. C. Greubel_, Sep 03 2019
%o A099761 (GAP) List([0..40], n-> (n*(n+2))^2); # _G. C. Greubel_, Sep 03 2019
%Y A099761 Cf. A005563.
%K A099761 nonn,easy
%O A099761 0,2
%A A099761 Kari Lajunen (Kari.Lajunen(AT)Welho.com), Nov 11 2004
%E A099761 Deleted a trivial formula which was based on another offset - _R. J. Mathar_, Dec 16 2009