

A188697


Expansion of (1+2*x^2)/(126*x+2*x^252*x^3+4*x^4).


1



1, 26, 676, 17576, 456972, 11881168, 308907672, 8031529376, 208817941280, 5429219088800, 141158464323104, 3670088041052160, 95421456259562432, 2480936209934965120, 64503778490067388160, 1677083603695215199744, 43603793136187040353536, 1133688727070116383116288, 29475649649828842801150464, 766360202350076625301264384
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OFFSET

0,2


COMMENTS

From the Noonan and Zeilberger link below, a(n) is the number of words in the 26letter English alphabet {A,B,C,...,X,Y,Z} that do not contain any of the "bad" words: PIPI or CACA or PICA or CAPI. The expected wait time to see an occurrence of one of any of these four words is G(1/26) = 114582. The expected wait time to see all four of these words is 979223595402/1028195 (approximately 952371).  Geoffrey Critzer, May 17 2014


LINKS



FORMULA

G.f.: (1+2*x^2)/(126*x+2*x^252*x^3+4*x^4).
a(0)=1, a(1)=26, a(2)=676, a(3)=17576, a(n)=26*a(n1)2*a(n2)+ 52*a(n3) 4*a(n4).  Harvey P. Dale, Oct 04 2014


MATHEMATICA

sol=Solve[{A==z^4z^2Az^2D, B==z^4z^2Bz^2C, C==z^4z^2Az^2D, D==z^4z^2Bz^2C}, {A, B, C, D}]; nn=20; CoefficientList[Series[1/(126zABCD)/.sol, {z, 0, nn}], z] (* Geoffrey Critzer, May 17 2014 *)
LinearRecurrence[{26, 2, 52, 4}, {1, 26, 676, 17576}, 30] (* Harvey P. Dale, Oct 04 2014 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



