# [seqfan] Re: Gen. Functs. A039219

Maximilian Hasler maximilian.hasler at gmail.com
Fri Sep 11 21:01:55 CEST 2009

```Dear seqfans,
don't waste your time to check, all other g.f. in this series are also wrong.
M.H.
PS: details below

For A039255 the given g.f. isn't OK, either.
In particular, it has the term  60 x^50  but  60 (and the 6 following
terms 61..66) are not in the sequence (60[10] = 50[12]).

The g.f. given in A039257 also includes the term
60*x^50
and followings, but 60, 61,... are not in the sequence

? (x*(x^8+2*x^6-x^5+2*x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)
+O(x^55)

%58 = ... 59*x^49 + 60*x^50 + 61*x^51 + 62*x^52 + 63*x^53 + 64*x^54 + O(x^55)

The g.f. given in A039261 contains terms  72*x^60 + ... which should
not be there :

(x*(x^8+x^6+x^5+x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)+O(x^65)

= .... + 71*x^59 + 72*x^60 + 73*x^61 + 74*x^62 + 75*x^63 + 76*x^64 + O(x^65)

The g.f. given in A039263 yields terms  72*x^60 +... which should not be there:

(x*(x^8+x^7+x^5+x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)+O(x^65)
%64 = ... + 69*x^58 + 71*x^59 + 72*x^60 + 73*x^61 + 74*x^62 + 75*x^63
+ 76*x^64 + 77*x^65 + 79*x^66 + 80*x^67 + 81*x^68 + 83*x^69 + 84*x^70
+ 85*x^71 + 86*x^72 + 87*x^73 + 88*x^74 + O(x^75)

The g.f. given in A039266 yields terms  84*x^70 +... which should not be there:

(x*(x^2+1)*(x^6+x^4+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)+O(x^75)
%65 = ...+ 83*x^69 + 84*x^70 + 85*x^71 + 86*x^72 + 87*x^73 + 88*x^74 + O(x^75)

The g.f. given in A039268 also yields terms  84*x^70 +... which should
not be there:

(x*(2*x^8-x^7+2*x^6+x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)
+O(x^85)
%67 = ... + 82*x^69 + 84*x^70 + 85*x^71 + 86*x^72 + 87*x^73 + 88*x^74
+ 89*x^75 + 90*x^76 + 92*x^77 + 93*x^78 + 94*x^79 + 96*x^80 + 97*x^81
+ 98*x^82 + 99*x^83 + 100*x^84 + O(x^85)

The g.f. given in A039270  yields terms  96*x^80 +... which should not be there:

(x*(x^2+x+1)*(x^6+x^2-x+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)+O(x^85)
%68 = ... + 95*x^79 + 96*x^80 + 97*x^81 + 98*x^82 + 99*x^83 + 100*x^84 + O(x^85)

The g.f. given in A039270  yields terms  96*x^80 +... which should not be there:

(x*(2*x^8+x^6+x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)
+ O(x^85)

The g.f. given in A039273  yields terms  108*x^90 +... which should
not be there:

(x*(2*x^8+x^6+x^4+x^2+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2)
+ O(x^95)
%70 = ... + 106*x^89 + 108*x^90 + 109*x^91 + 110*x^92 + 111*x^93 +
112*x^94 + O(x^95)

```