A014796 Squares of even tetrahedral numbers (A015220).
0, 16, 100, 400, 3136, 7056, 14400, 48400, 81796, 132496, 313600, 462400, 665856, 1299600, 1768900, 2371600, 4096576, 5290000, 6760000, 10732176, 13351716, 16483600, 24601600, 29767936, 35808256, 50979600, 60372900, 71166096, 97614400, 113635600, 131790400, 175403536
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-15,15,0,20,-20,0,-15,15,0,6,-6,0,-1,1).
Programs
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Mathematica
Select[Binomial[Range[0,40]+2,3],EvenQ]^2 (* Harvey P. Dale, Jan 19 2012 *)
Formula
From Amiram Eldar, Mar 07 2022: (Start)
a(n) = A015220(n)^2.
Sum_{n>=1} 1/a(n) = 27*(Pi^2 + Pi - 13)/4. (End)
a(n) = a(n-1) + 6*a(n-3) - 6*a(n-4) - 15*a(n-6) + 15*a(n-7) + 20*a(n-9) - 20*a(n-10) - 15*a(n-12) + 15*a(n-13) + 6*a(n-15) - 6*a(n-16) - a(n-18) + a(n-19). - Wesley Ivan Hurt, Jul 16 2025
Extensions
More terms from Erich Friedman
a(0) and more terms from Amiram Eldar, Mar 07 2022