OFFSET
0,3
COMMENTS
The Dira (2017) article describes this as the self-convolution of A001045, but it is really the self-composition. - N. J. A. Sloane, Apr 07 2019, following a suggestion from Ilya Gutkovskiy. Note that A073371 is the convolution of A001045(n+1) with itself, with g.f.: g(x)^2/x^2, where g(x) = g.f. of A001045).
The Dira (2017) article contains on pages 851 and 852 several other sequences that could be added to the OEIS.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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 (3,4,-6,-4).
FORMULA
G.f.: (-2*x^3-x^2+x)/(4*x^4+6*x^3-4*x^2-3*x+1).
a(n) = 3*a(n-1) + 4*a(n-2) - 6*a(n-3) - 4*a(n-4). - Vincenzo Librandi, Mar 30 2018
MAPLE
f:=proc(a, b) local t1;
t1:=(x-a*x^2-b*x^3)/(1-3*a*x+(2*a^2-3*b)*x^2+3*a*b*x^3 + b^2*x^4);
lprint(t1);
series(t1, x, 50);
seriestolist(%);
end;
f(1, 2);
MATHEMATICA
CoefficientList[Series[(-2 x^3 - x^2 + x) / (4 x^4 + 6 x^3 - 4 x^2 - 3 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 30 2018 *)
PROG
(Magma) I:=[0, 1, 2, 8]; [n le 4 select I[n] else 3*Self(n-1)+4*Self(n-2)-6*Self(n-3)-4*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Mar 30 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 29 2018
STATUS
approved