A200543 Product of tribonacci numbers: a(n) = A000073(n+2)*A000213(n).

1, 1, 2, 12, 35, 117, 408, 1364, 4617, 15645, 52882, 178920, 605331, 2047705, 6927424, 23435384, 79281057, 268206185, 907335090, 3069491988, 10384017875, 35128880685, 118840150776, 402033352684, 1360069088841, 4601080767717, 15565344749410, 52657184101648, 178137977818211, 602636462317425

Offset: 0

Author

Paul D. Hanna, Nov 19 2011

Keywords

• nonn
• easy

Comments

The g.f. of the tribonacci numbers are as follows: g.f. for A000073 is x^2/(1-x-x^2-x^3), and g.f. for A000213 is (1-x^2)/(1-x-x^2-x^3).

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 35*x^4 + 117*x^5 + 408*x^6 +...
where A(x) = 1*1 + 1*1*x + 2*1*x^2 + 4*3*x^3 + 7*5*x^4 + 13*9*x^5 + 24*17*x^6 + 44*31*x^7 + 81*57*x^8 + 149*105*x^9 +...+ A000073(n+2)*A000213(n)*x^n +...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,6,-1,0,-1).

Crossrefs

Cf. A000073, A000213.

Programs

PARI

{a(n)=polcoeff((1-x-3*x^2-x^3)/((1-3*x-x^2-x^3)*(1+x+x^2-x^3)+x*O(x^n)),n)}

Formula

G.f.: (1 - x - 3*x^2 - x^3) / ((1 - 3*x - x^2 - x^3)*(1 + x + x^2 - x^3)).