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 A006044 A traffic light problem. (Formerly M4290) 6

%I M4290

%S 6,96,960,7680,53760,344064,2064384,11796480,64880640,346030080,

%T 1799356416,9160359936,45801799680,225485783040,1095216660480,

%U 5257039970304,24970939858944,117510305218560,548381424353280,2539871860162560,11683410556747776,53409876830846976

%N A traffic light problem.

%C I have derived the terms in a rather laborious 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, 6*x^4/(1+4*x)^4. The Maple program, probably not the simplest one, is for the signed sequence. - _Emeric Deutsch_, Apr 29 2004

%C Fourth column of triangle A152818 (1,1,1,1,4,2,1,12,...). [_Paul Curtz_, Dec 17 2008]

%C Column 3 of square array A152818. [_Omar E. Pol_, Jan 07 2009]

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006044/b006044.txt">Table of n, a(n) for n = 4..1000</a>

%H F. A. Haight, <a href="http://www.jstor.org/stable/2333538">Overflow at a traffic light</a>, Biometrika, 46 (1959), 420-424.

%H F. A. Haight, <a href="/A001787/a001787_3.pdf">Overflow at a traffic light</a>, Biometrika, 46 (1959), 420-424. (Annotated scanned copy)

%H F. A. Haight, <a href="/A001787/a001787_2.pdf">Letter to N. J. A. Sloane, n.d.</a>

%F It seems that the g.f. is 6*x^4/(1-4*x)^4 (for the positive sequence), a(n)=6*A038846(n).. - _Emeric Deutsch_, Apr 29 2004

%F a(n) = 4^(n-4)*(n-3)*(n-2)*(n-1). [_Omar E. Pol_, Jan 04 2009]

%F a(n) = 4^(n-4)*(n-1)!/(n-4)!. [_Omar E. Pol_, Jan 15 2009]

%p 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);

%o (MAGMA) [4^(n-4)*(n-3)*(n-2)*(n-1): n in [4..30]]; // _Vincenzo Librandi_, Aug 14 2011

%Y Cf. A152818. [_Omar E. Pol_, Jan 05 2009]

%Y Cf. A000142, A006043, A152818, A154120. [_Omar E. Pol_, Jan 15 2009]

%K nonn,easy

%O 4,1

%A _N. J. A. Sloane_.

%E More terms from _Emeric Deutsch_, Apr 29 2004

%E Deleted erroneous reference Martin J. Erickson (erickson(AT)truman.edu), Nov 03 2010

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)