login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 0
0, 1, 3, 13, 44, 122, 292, 631, 1267, 2411, 4408, 7820, 13560, 23109, 38867, 64721, 106964, 175782, 287660, 469275, 763795, 1241071, 2014128, 3265848, 5292144, 8571817, 13879587, 22468981, 36368252, 58859186, 95251828, 154138015 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+1+n^3, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
LINKS
FORMULA
a(n)=5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).
G.f.: -x*(7*x^2-2*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012]
MATHEMATICA
(See A193008.)
CROSSREFS
Sequence in context: A208060 A284194 A209296 * A058407 A095863 A136520
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 15 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 8 14:02 EDT 2023. Contains 363165 sequences. (Running on oeis4.)