cp's OEIS Frontend

A081190 8th binomial transform of (1,0,1,0,1,.....), A059841.

%I A081190 #21 Sep 08 2022 08:45:09
%S A081190 1,8,65,536,4481,37928,324545,2803256,24405761,213887048,1884629825,
%T A081190 16679193176,148135411841,1319377419368,11777507763905,
%U A081190 105319346802296,943126559710721,8454906106826888,75861524447454785,681125306429182616
%N A081190 8th binomial transform of (1,0,1,0,1,.....), A059841.
%C A081190 Binomial transform of A081189.
%C A081190 a(n) is also the number of words of length n over an alphabet of nine 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. For a formulation in terms of maps see a Geoffrey Critzer comment in A081189. - _Wolfdieter Lang_, Jul 17 2017
%H A081190 Vincenzo Librandi, <a href="/A081190/b081190.txt">Table of n, a(n) for n = 0..200</a>
%H A081190 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-63).
%F A081190 a(n) = 16*a(n-1) -63*a(n-2), a(0)=1, a(1)=8.
%F A081190 G.f.: (1-8*x)/((1-7*x)*(1-9*x)).
%F A081190 E.g.f. exp(8*x) * cosh(x).
%F A081190 a(n) = 7^n/2 + 9^n/2.
%t A081190 CoefficientList[Series[(1 - 8 x) / ((1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081190 LinearRecurrence[{16,-63},{1,8},20] (* _Harvey P. Dale_, Apr 04 2017 *)
%o A081190 (Magma) [7^n/2 + 9^n/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081190 Cf. A007582, A060531, A081189.
%K A081190 easy,nonn
%O A081190 0,2
%A A081190 _Paul Barry_, Mar 11 2003