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A006044 A traffic light problem.
(Formerly M4290)
6, 96, 960, 7680, 53760, 344064, 2064384, 11796480, 64880640, 346030080, 1799356416, 9160359936, 45801799680, 225485783040, 1095216660480, 5257039970304, 24970939858944, 117510305218560, 548381424353280, 2539871860162560, 11683410556747776, 53409876830846976 (list; graph; refs; listen; history; text; internal format)



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

Fourth column of triangle A152818 (1,1,1,1,4,2,1,12,...). [Paul Curtz, Dec 17 2008]

Column 3 of square array A152818. [Omar E. Pol, Jan 07 2009]


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


Vincenzo Librandi, Table of n, a(n) for n = 4..1000

F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.

F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424. (Annotated scanned copy)

F. A. Haight, Letter to N. J. A. Sloane, n.d.


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

a(n) = 4^(n-4)*(n-3)*(n-2)*(n-1). [Omar E. Pol, Jan 04 2009]

a(n) = 4^(n-4)*(n-1)!/(n-4)!. [Omar E. Pol, Jan 15 2009]


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);


(MAGMA) [4^(n-4)*(n-3)*(n-2)*(n-1): n in [4..30]]; // Vincenzo Librandi, Aug 14 2011


Cf. A152818. [Omar E. Pol, Jan 05 2009]

Cf. A000142, A006043, A152818, A154120. [Omar E. Pol, Jan 15 2009]

Sequence in context: A055358 A030989 A288845 * A202078 A227262 A001805

Adjacent sequences:  A006041 A006042 A006043 * A006045 A006046 A006047




N. J. A. Sloane.


More terms from Emeric Deutsch, Apr 29 2004

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



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Last modified November 17 19:40 EST 2017. Contains 294834 sequences.