Search: id:A006044
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%I A006044 M4290
%S A006044 6,96,960,7680,53760,344064,2064384,11796480,64880640,346030080,1799356416,
               9160359936,
%T A006044 45801799680,225485783040,1095216660480,5257039970304,24970939858944,117510305218560,
%U A006044 548381424353280,2539871860162560,11683410556747776,53409876830846976
%V A006044 6,96,960,7680,53760,344064,2064384,11796480,64880640,346030080,1799356416,
               9160359936,
%W A006044 45801799680,225485783040,1095216660480,5257039970304,24970939858944,117510305218560,
%X A006044 548381424353280,2539871860162560,11683410556747776,53409876830846976
%N A006044 A traffic light problem.
%C A006044 I have derived the terms in a rather laborius way (see the Maple program), 
               following the Haight paper, where the signed sequence occurs. The 
               simple g.f. for the positive sequence is conjectured by analogy with 
               A006043. For the signed sequence it is, obviously, 6x^4/(1+4x)^4. 
               The Maple program, probably not the simplest one, is for the signed 
               sequence. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004
%C A006044 Fourth column of triangle A152818 (1,1,1,1,4,2,1,12,) or A152818(9),A152818(13),
               A152818(18),A152818(24),A152818(31),. See submitted A153027. Linked 
               to factorial polynomials A152650/A152656 (also not simplified A009998/
               A119502, correct in it bad value A119052). [From Paul Curtz (bpcrtz(AT)free.fr), 
               Dec 17 2008]
%C A006044 Column 3 of square array A152818. [From Omar E. Pol (info(AT)polprimos.com), 
               Jan 07 2009]
%D A006044 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006044 F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.
%F A006044 It seems that G.f.= 6x^4/(1-4x)^4 (for the positive sequence). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004
%F A006044 a(n) = 4^(n-4)*(n-3)*(n-2)*(n-1). [From Omar E. Pol (info(AT)polprimos.com), 
               Jan 04 2009] E.g. a(6)=960 because 4^(6-4)*(6-3)*(6-2)*(6-1) = 4^2*3*4*5 
               = 16*3*4*5 = 960. [From Omar E. Pol (info(AT)polprimos.com), Jan 
               04 2009]
%F A006044 a(n) = 4^(n-4)*(n-1)!/(n-4)!. [From Omar E. Pol (info(AT)polprimos.com), 
               Jan 15 2009]
%p A006044 A:=(u,r)->r*u^(u-r-1)/(u-r)!: a:=proc(i,j) if j>i+1 then 0 elif j=i+1 
               then 1 else A(z-j+1,z-i) fi end: with(linalg): B:=proc(z,x) if z=x 
               then 1 else (-1)^(z+x)*det(matrix(z-x,z-x,a)) fi end: seq(expand(subs(z=k,
               (z-1)!*B(k,4))),k=4..26);
%Y A006044 Cf. A152818. [From Omar E. Pol (info(AT)polprimos.com), Jan 05 2009]
%Y A006044 Cf. A000142, A006043, A152818, A154120. [From Omar E. Pol (info(AT)polprimos.com), 
               Jan 15 2009]
%Y A006044 Sequence in context: A115400 A055358 A030989 this_sequence A001805 A139743 
               A156460
%Y A006044 Adjacent sequences: A006041 A006042 A006043 this_sequence A006045 A006046 
               A006047
%K A006044 sign
%O A006044 4,1
%A A006044 N. J. A. Sloane (njas(AT)research.att.com).
%E A006044 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004

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