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

0,3

Links

Table of n, a(n) for n=0..29.

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).

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.

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 *)

Crossrefs

Cf. A000045, A001045.

Sequence in context: A116387 A337805 A294006 * A294007 A294008 A294009

Adjacent sequences: A322570 A322571 A322572 * A322574 A322575 A322576

Keyword

nonn

Author

Oboifeng Dira, Aug 29 2019

Extensions

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

Status

approved