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

%I A322573 #37 Nov 10 2019 12:02:53
%S A322573 0,1,2,7,22,73,240,793,2618,8647,28558,94321,311520,1028881,3398162,
%T A322573 11223367,37068262,122428153,404352720,1335486313,4410811658,
%U A322573 14567921287,48114575518,158911647841,524849519040,1733460204961,5725230133922,18909150606727,62452681954102,206267196469033
%N A322573 G.f. = g(f(x)), where f(x) = g.f. of Fibonacci sequence A000045 and g(x) = g.f. of Jacobsthal sequence A001045.
%H A322573 Oboifeng Dira, <a href="http://www.seams-bull-math.ynu.edu.cn/downloadfile.jsp?filemenu=_201706&amp;filename=07_41(6).pdf">A Note on Composition and Recursion</a>, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
%H A322573 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-3,-1).
%F A322573 G.f.: x*(1-x-x^2)/((1-3*x-x^2)*(1-x^2)).
%F A322573 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.
%p A322573 g:=x->x/(1-x-2*x^2):
%p A322573 f:=x->x/(1-x-x^2):
%p A322573 C:=n->coeff(series(g(f(x)),x,n+1),x,n):
%p A322573 seq(C(n),n=0..30);
%t A322573 LinearRecurrence[{3, 2, -3, -1}, {0, 1, 2, 7}, 30] (* _Jean-François Alcover_, Nov 10 2019 *)
%Y A322573 Cf. A000045, A001045.
%K A322573 nonn
%O A322573 0,3
%A A322573 _Oboifeng Dira_, Aug 29 2019
%E A322573 Edited by _N. J. A. Sloane_, Sep 23 2019