login
A014796
Squares of even tetrahedral numbers (A015220).
2
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
0,2
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).
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
MATHEMATICA
Select[Binomial[Range[0, 40]+2, 3], EvenQ]^2 (* Harvey P. Dale, Jan 19 2012 *)
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from Erich Friedman
a(0) and more terms from Amiram Eldar, Mar 07 2022
STATUS
approved