STATUS
editing
approved
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0 if pronounced name of n-th letter of English alphabet begin with a vowel sound, otherwise 1. Different from A054638.
(history; published version)
(history; published version)
AUTHOR
_Jim Nastos (nastos(AT)gmail.com), _, Jun 11 2003
STATUS
approved
editing
KEYWORD
fini,full,nonn,word,new
AUTHOR
Jim Nastos (nastos(AT)cs.ualbertagmail.cacom), Jun 11 2003
NAME
0 if pronounced name of n-th letter of English alphabet begin with a vowel sound, otherwise 1. Different from A054638.
KEYWORD
fini,full,nonn,word,new
NAME
Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=b*nu(n-1)+lambda*(n-1)_q*nu(n-2) with (b,lambda)=(1,1),where (n)_q=(1+q+...+q^(n-1)) and q is a root of unity.
0 if pronounced name of n-th letter of English alphabet begin with a vowel sound, otherwise 1.
DATA
1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1
OFFSET
0,3
1,1
COMMENTS
Instead of listing the coefficients of the highest power of q in each nu(n), if we listed the coefficients of the lowest power of q(i.e. constant terms), we get the Fibonacci numbers described by f(0)=1, f(1)=1, for n>=2, f(n)=f(n-1)+f(n-2).
LINKS
M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, <a href="http://front.math.ucdavis.edu/math.QA/0204075">Lifting of Nichols Algebras of Type $B_2$</a>
FORMULA
for given b and lambda, the recurrence relation is given by; t(0)=1, t(1)=b, t(2)=b^2+lambda and for n>=3, t(n)=lambda*T(n-2)
a(n)=(3-2*0^n +(-1)^n)/2. G.f. is (1+x+x^2)/(1-x^2). E.g.f. (3exp(x)-2exp(0)+exp(-x))/2. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2003
EXAMPLE
nu(0)=1 nu(1)=1; nu(2)=2; nu(3)=3+q; nu(4)=5+3q+2q^2; nu(5)=8+7q+6q^2+4q^3+q^4; nu(6)=13+15q+16q^2+14q^3+11q^4+5q^5+2q^6; by listing the coefficients of the highest power in each nu(n), we get, 1,1,2,1,2,1,2,...
KEYWORD
fini,full,nonn,newword
AUTHOR
Y. Kelly Itakura Jim Nastos (yitkrnastos(AT)mtacs.ualberta.ca), Aug 21 2002Jun 11 2003
NAME
Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b and for n>=2, nu(n)=b*nu(n-1)+lambda*(n-1)_q*nu(n-2) with (b,lambda)=(1,1),where (n)_q=(1+q+...+q^(n-1)) and q is a root of unity.
DATA
1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
OFFSET
0,3
COMMENTS
Instead of listing the coefficients of the highest power of q in each nu(n), if we listed the coefficients of the lowest power of q(i.e. constant terms), we get the Fibonacci numbers described by f(0)=1, f(1)=1, for n>=2, f(n)=f(n-1)+f(n-2).
LINKS
M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, <a href="http://front.math.ucdavis.edu/math.QA/0204075">Lifting of Nichols Algebras of Type $B_2$</a>
FORMULA
for given b and lambda, the recurrence relation is given by; t(0)=1, t(1)=b, t(2)=b^2+lambda and for n>=3, t(n)=lambda*T(n-2)
a(n)=(3-2*0^n +(-1)^n)/2. G.f. is (1+x+x^2)/(1-x^2). E.g.f. (3exp(x)-2exp(0)+exp(-x))/2. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2003
EXAMPLE
nu(0)=1 nu(1)=1; nu(2)=2; nu(3)=3+q; nu(4)=5+3q+2q^2; nu(5)=8+7q+6q^2+4q^3+q^4; nu(6)=13+15q+16q^2+14q^3+11q^4+5q^5+2q^6; by listing the coefficients of the highest power in each nu(n), we get, 1,1,2,1,2,1,2,...
CROSSREFS
Cf. A000045.
KEYWORD
nonn
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
STATUS
approved