A322573 G.f. = g(f(x)), where f(x) = g.f. of Fibonacci sequence A000045 and g(x) = g.f. of Jacobsthal sequence A001045.

0, 1, 2, 7, 22, 73, 240, 793, 2618, 8647, 28558, 94321, 311520, 1028881, 3398162, 11223367, 37068262, 122428153, 404352720, 1335486313, 4410811658, 14567921287, 48114575518, 158911647841, 524849519040, 1733460204961, 5725230133922, 18909150606727, 62452681954102, 206267196469033

Offset: 0

Author

Oboifeng Dira, Aug 29 2019

Keywords

• nonn

Links

• Oboifeng Dira, A Note on Composition and Recursion, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
• Index entries for linear recurrences with constant coefficients, signature (3,2,-3,-1).

Crossrefs

Cf. A000045, A001045.

Programs

Maple

g:=x->x/(1-x-2*x^2):
f:=x->x/(1-x-x^2):
C:=n->coeff(series(g(f(x)),x,n+1),x,n):
seq(C(n),n=0..30);

Mathematica

LinearRecurrence[{3, 2, -3, -1}, {0, 1, 2, 7}, 30] (* Jean-François Alcover, Nov 10 2019 *)

Formula

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

a(n) = 3a(n-1)+2a(n-2)-3a(n-3)-a(n-4), a(0)=0, a(1)=1, a(2)=2, a(3)=7.

Extensions

Edited by N. J. A. Sloane, Sep 23 2019