OFFSET
0,21
COMMENTS
A121262 convolved with A079998. The two sequences have very simple generating functions and can be mapped to the numeric partitions 4=4 and 5=5 respectively.
Number of partitions of n into parts 4 and 5. - Joerg Arndt, Aug 28 2015
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
A. V. Kitaev and A. Vartanian, Algebroid Solutions of the Degenerate Third Painlevé Equation for Vanishing Formal Monodromy Parameter, arXiv:2304.05671 [math.CA], 2023. See p. 20.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,0,0,0,-1).
FORMULA
1 followed by the Euler transform of the finite sequence [0,0,0,1,1].
G.f.: 1/((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2+x^3+x^4)). [R. J. Mathar, Oct 07 2009]
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=0, a(7)=0, a(8)=1, a(n) = a(n-4)+a(n-5)-a(n-9), n>8. - Harvey P. Dale, Aug 16 2012
a(n) = floor((n+4)/4) - floor((n+4)/5). - Wesley Ivan Hurt, Aug 27 2015
a(n)+a(n-2) = A008616(n). - R. J. Mathar, Jun 23 2021
MAPLE
A165190:=n->floor((n+4)/4) - floor((n+4)/5): seq(A165190(n), n=0..100); # Wesley Ivan Hurt, Aug 27 2015
MATHEMATICA
CoefficientList[Series[1/((1-x^4)(1-x^5)), {x, 0, 110}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 0, 1}, 110] (* Harvey P. Dale, Aug 16 2012 *)
Table[Floor[(n + 4)/4] - Floor[(n + 4)/5], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 27 2015 *)
PROG
(Magma) [Floor((n+4)/4) - Floor((n+4)/5) : n in [0..100]]; // Wesley Ivan Hurt, Aug 27 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alford Arnold, Sep 24 2009
EXTENSIONS
Removed duplicate of comment in A165188; Euler transform formula corrected - R. J. Mathar, Oct 07 2009
STATUS
approved