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 A014738 #22 Jul 02 2025 16:01:55
%S A014738 36,100,784,1296,4356,6084,14400,18496,36100,44100,76176,90000,142884,
%T A014738 164836,246016,278784,396900,443556,608400,672400,894916,980100,
%U A014738 1272384,1382976,1758276,1898884,2371600,2547216,3132900,3348900
%N A014738 Squares of even triangular numbers.
%H A014738 Harvey P. Dale, <a href="/A014738/b014738.txt">Table of n, a(n) for n = 0..1000</a>
%H A014738 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).
%F A014738 a(n) = A014494(n + 1)^2. - _Sean A. Irvine_, Nov 18 2018
%F A014738 From _G. C. Greubel_, Jul 24 2019: (Start)
%F A014738 G.f.: 4*x*(9 +16*x +135*x^2 +64*x^3 +135*x^4 +16*x^5 +9*x^6)/((1-x)^5*(1+x)^4).
%F A014738 E.g.f.: x*(35+41*x+36*x^2+4*x^3)*cosh(x) + (1+9*x+77*x^2+28*x^3+4*x^4)* sinh(x). (End)
%F A014738 From _Amiram Eldar_, Mar 06 2022: (Start)
%F A014738 Sum_{n>=0} 1/a(n) = 7*Pi^2/12 + 2*Pi - 12.
%F A014738 Sum_{n>=0} (-1)^n/a(n) = 12 - 4*G - 12*log(2), where G is Catalan's constant (A006752). (End)
%t A014738 Select[Accumulate[Range[100]],EvenQ]^2 (* _Harvey P. Dale_, Oct 09 2012 *)
%o A014738 (PARI) vector(30, n, ((2*n+1)*(2*n+1-(-1)^n))^2/4) \\ _G. C. Greubel_, Jul 24 2019
%o A014738 (Magma) [((2*n+1)*(2*n+1-(-1)^n))^2/4: n in [1..30]]; // _G. C. Greubel_, Jul 24 2019
%o A014738 (Sage) [((2*n+1)*(2*n+1-(-1)^n))^2/4 for n in (1..30)] # _G. C. Greubel_, Jul 24 2019
%o A014738 (GAP) List([1..30], n-> ((2*n+1)*(2*n+1-(-1)^n))^2/4); # _G. C. Greubel_, Jul 24 2019
%Y A014738 Cf. A006752, A014494, A014736.
%K A014738 nonn,easy
%O A014738 0,1
%A A014738 _Mohammad K. Azarian_
%E A014738 More terms from _James Sellers_