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%I A081188 #27 Sep 08 2022 08:45:09
%S A081188 1,6,37,234,1513,9966,66637,450834,3077713,21153366,146120437,
%T A081188 1013077434,7042713913,49054856766,342163294237,2389039544034,
%U A081188 16692759230113,116696726720166,816114147588037,5708984335850634
%N A081188 6th binomial transform of (1,0,1,0,1,.....), A059841.
%C A081188 Binomial transform of A081187.
%C A081188 a(n) is also the number of words of length n over an alphabet of seven letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 11- letter word cases. - _Wolfdieter Lang_, Jul 17 2017
%H A081188 Vincenzo Librandi, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EwODExODgvYjA4MTE4OC50eHQ">Table of n, a(n) for n = 0..200</a>
%H A081188 Takao Komatsu, <a href="/load/view.php?a=aHR0cHM6Ly9kb2kub3JnLzEwLjIyNDM2L2puc2EuMDEyLjEyLjA1">Some recurrence relations of poly-Cauchy numbers</a>, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.
%H A081188 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlYyNvcmRlcl8wMg">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35).
%F A081188 a(n) = 12*a(n-1) -35*a(n-2), a(0)=1, a(1)=6.
%F A081188 G.f.: (1-6*x)/((1-5*x)*(1-7*x)).
%F A081188 E.g.f.: exp(6*x)*cosh(x).
%F A081188 a(n) = 5^n/2 + 7^n/2.
%t A081188 CoefficientList[Series[(1 - 6 x) / ((1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081188 LinearRecurrence[{12,-35},{1,6},30] (* _Harvey P. Dale_, Mar 24 2016 *)
%o A081188 (Magma) [5^n/2+7^n/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 07 2013
%o A081188 (PARI) a(n)=5^n/2+7^n/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A081188 Cf. A007582, A081186, A081189.
%K A081188 nonn,easy
%O A081188 0,2
%A A081188 _Paul Barry_, Mar 11 2003

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