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A014738
Squares of even triangular numbers.
3
36, 100, 784, 1296, 4356, 6084, 14400, 18496, 36100, 44100, 76176, 90000, 142884, 164836, 246016, 278784, 396900, 443556, 608400, 672400, 894916, 980100, 1272384, 1382976, 1758276, 1898884, 2371600, 2547216, 3132900, 3348900
OFFSET
0,1
FORMULA
a(n) = A014494(n + 1)^2. - Sean A. Irvine, Nov 18 2018
From G. C. Greubel, Jul 24 2019: (Start)
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).
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)
From Amiram Eldar, Mar 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 7*Pi^2/12 + 2*Pi - 12.
Sum_{n>=0} (-1)^n/a(n) = 12 - 4*G - 12*log(2), where G is Catalan's constant (A006752). (End)
MATHEMATICA
Select[Accumulate[Range[100]], EvenQ]^2 (* Harvey P. Dale, Oct 09 2012 *)
PROG
(PARI) vector(30, n, ((2*n+1)*(2*n+1-(-1)^n))^2/4) \\ G. C. Greubel, Jul 24 2019
(Magma) [((2*n+1)*(2*n+1-(-1)^n))^2/4: n in [1..30]]; // G. C. Greubel, Jul 24 2019
(Sage) [((2*n+1)*(2*n+1-(-1)^n))^2/4 for n in (1..30)] # G. C. Greubel, Jul 24 2019
(GAP) List([1..30], n-> ((2*n+1)*(2*n+1-(-1)^n))^2/4); # G. C. Greubel, Jul 24 2019
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from James A. Sellers
STATUS
approved