A015220 Even tetrahedral numbers.

0, 4, 10, 20, 56, 84, 120, 220, 286, 364, 560, 680, 816, 1140, 1330, 1540, 2024, 2300, 2600, 3276, 3654, 4060, 4960, 5456, 5984, 7140, 7770, 8436, 9880, 10660, 11480, 13244, 14190, 15180, 17296, 18424, 19600, 22100, 23426, 24804, 27720, 29260, 30856, 34220, 35990

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).

Crossrefs

Cf. A000292, A004772, A015219.

Programs

Mathematica

LinearRecurrence[{1,0,3,-3,0,-3,3,0,1,-1},{0,4,10,20,56,84,120,220,286,364},41] (* Ant King, Oct 19 2012 *)
Select[Table[(Times@@(n+{0,1,2}))/6,{n,0,60}],EvenQ] (* Harvey P. Dale, Jan 22 2013 *)

Formula

From Ant King, Oct 19 2012: (Start)

a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - 3*a(n-6) + 3*a(n-7) + a(n-9) - a(n-10).

a(n) = 64 + 3*a(n-3) - 3*a(n-6) + a(n-9).

G.f.: 2*x*(2+3*x+5*x^2+12*x^3+5*x^4+3*x^5+2*x^6) / ((1-x)^4*(1+x+x^2)^3).

Sum_{n>=1} 1/a(n) = 3/2*(1-log(2)). (End)

From Amiram Eldar, Mar 07 2022: (Start)

a(n) = A000292(A004772(n+1)).

Sum_{n>=1} (-1)^(n+1)/a(n) = 3*log(2) - 15/2 + 9*sqrt(2)*log(sqrt(2)+1)/2. (End)

Extensions

More terms from Erich Friedman

a(0) prepended by Amiram Eldar, Mar 07 2022