A107240 Sum of squares of first n tribonacci numbers (A000213).

1, 2, 3, 12, 37, 118, 407, 1368, 4617, 15642, 52891, 178916, 605325, 2047726, 6927407, 23435376, 79281105, 268206130, 907335091, 3069492092, 10384017717, 35128880742, 118840150983, 402033352264, 1360069089113, 4601080768074

Offset: 1

Author

Jonathan Vos Post, May 14 2005

Keywords

• easy
• nonn

Examples

			a(6) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 = 118.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• M. Feinberg, Fibonacci-Tribonacci, Fib. Quart. 1(3) (1963), 71-74.
• Eric Weisstein's World of Mathematics, Tribonacci Number.
• Index entries for linear recurrences with constant coefficients, signature (3, 1, 3, -7, 1, -1, 1).

Crossrefs

Cf. A000213, A001654, A107239, A107241-A107247.

Programs

Mathematica

Accumulate[LinearRecurrence[{1,1,1},{1,1,1},30]^2] (* Harvey P. Dale, Nov 11 2011 *)
LinearRecurrence[{3, 1, 3, -7, 1, -1, 1},{1, 2, 3, 12, 37, 118, 407},26] (* Ray Chandler, Aug 02 2015 *)

Formula

a(n) = Sum_{i=1..n} A000213(i)^2.

a(n)= 3*a(n-1) +a(n-2) +3*a(n-3) -7*a(n-4) +a(n-5) -a(n-6) +a(n-7). G.f.: (x^3-x^2+3*x-1)*(1+x)^2/((x-1)*(x^3+x^2+3*x-1)*(x^3-x^2-x-1)). - R. J. Mathar, Aug 11 2009