A338192 Sum of Fibonacci and tribonacci numbers: a(n) = A000073(n) + A000045(n).

0, 1, 2, 3, 5, 9, 15, 26, 45, 78, 136, 238, 418, 737, 1304, 2315, 4123, 7365, 13193, 23694, 42655, 76958, 139126, 251974, 457112, 830501, 1510930, 2752175, 5018581, 9160293, 16734631, 30595694, 55976389, 102474674, 187700488, 343973242, 630623826, 1156594669

Offset: 0

Author

Gary Detlefs, Oct 15 2020

Keywords

• nonn
• easy

Comments

In general, the sum of a second-order sequence with signature (a,b) and a third-order sequence with signature (x,y,z) will be a fifth-order sequence with signature (a+x,-x*a+b+y, -y*a+z-b*x,-a*z-b*y,-b*z). In this instance, a=b=x=y=z=1 resulting in a signature of (2,1,-1,-2,-1).

Links

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

Crossrefs

Cf. A000045, A000073.

Programs

Mathematica

LinearRecurrence[{2, 1, -1, -2, -1}, {0, 1, 2, 3, 5}, 50] (* Amiram Eldar, Oct 15 2020 *)

Formula

a(n) = A000073(n) + A000045(n).

a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) for n > 4 with a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=5.

G.f.: x*(1 - 2*x^2 - 2*x^3)/(1 - 2*x - x^2 + x^3 + 2*x^4 + x^5). - Stefano Spezia, Oct 15 2020