A006044 - OEIS

%I M4290 #63 Jan 08 2023 02:39:53

%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(n) = 4^(n-4)*(n-1)*(n-2)*(n-3).

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

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

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-96,256,-256).

%F G.f. = 6*x^4/(1-4*x)^4. - _Emeric Deutsch_, Apr 29 2004

%F a(n) = 6*A038846(n). - _R. J. Mathar_ , Mar 22 2013

%F E.g.f.: (3 + exp(4*x)*(32*x^3 - 24*x^2 + 12*x - 3))/128. - _Stefano Spezia_, Jan 01 2023

%F From _Amiram Eldar_, Jan 08 2023: (Start)

%F Sum_{n>=4} 1/a(n) = 18*log(4/3) - 5.

%F Sum_{n>=4} (-1)^n/a(n) = 50*log(5/4) - 11. (End)

%t a[n_] := 4^(n - 4)*(n - 1)*(n - 2)*(n - 3); Array[a, 25, 4] (* _Amiram Eldar_, Jan 08 2023 *)

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

%Y Cf. A000142, A006043, A038846, A154120.

%Y Column k=3 of square array A152818. - _Paul Curtz_, Dec 17 2008 [corrected by _Omar E. Pol_, Jan 07 2009]

%K nonn,easy

%O 4,1

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Apr 29 2004

%E Erroneous reference deleted by Martin J. Erickson (erickson(AT)truman.edu), Nov 03 2010

%E Entry revised by _N. J. A. Sloane_, Dec 27 2021