A006336 - Unexpected Relation to Golden Ratio?
T. D. Noe
noe at sspectra.com
Mon Jul 23 21:39:53 CEST 2007
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concerning the "duplicates"
http://www.research.att.com/~njas/sequences/?q=id:A087186|id:A087189
I think all terms of the second one are wrong.
A087189(1) should be = (A005191(3)-1)/2/3^2 = 1
A087189(2) should be = (A005191(7)-1)/2/7^2 = 83
etc, instead of what is listed :
A087189 2,4,31,304,40044,500522,86094668,1167752848,225001039696,
Thus these are no duplicates at all. PARI code :
A087189(n) = local(p=prime(n+2-(n==1))); (A005191(p)-1)/2/p^2
A005191(n) = sum(k=0,(2*n)\5,binomial(n,k)*binomial(-n,2*n-5*k))
attached both sequences up to n=100 ; below the corrected entry for
the wrong one.
M.H.
%I A087189
%S A087189 1, 83, 16907, 279021, 89444018, 1695011087, 658067703933,
5768410509553937, 122108313460051500, 1226978854222034501448,
593538703869555995238872, 13175226571428140572866093,
6594852118968926152838341468, 76339779380132942579800334346403
%N A087189 (P(p)-1)/2/p^2 where p runs through the odd primes
different from 5 and P(k) is
the k-th central pentanomial coefficient (A005191).
%o A087189 (PARI) A087189(n) = local(p=prime(n+2-(n==1)));
(A005191(p)-1)/2/p^2 \\ - M.F. Hasler
%Y A087189 Adjacent sequences: A087186 A087187 A087188 this_sequence
A087190 A087191 A087192
%Y A087189 Sequence in context: A018294 A051569 A087186 this_sequence
A051759 A051570 A082913
%K A087189 nonn
%O A087189 1,1
%A A087189 Benoit Cloitre (abmt(AT)wanadoo.fr), Oct 19 2003
%E A087189 Corrected and extended by Maximilian F. Hasler
(Maximilian.Hasler at gmail.com), Jul 23 2007
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