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

0,2

Links

Table of n, a(n) for n=0..44.

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

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)

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 *)

Crossrefs

Cf. A000292, A004772, A015219.

Sequence in context: A056412 A032275 A220828 * A047199 A038065 A249975

Adjacent sequences: A015217 A015218 A015219 * A015221 A015222 A015223

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

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

Status

approved