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A177187 Union of A057080 and A001090.

%I A177187 #21 Apr 11 2024 04:42:22
%S A177187 1,1,9,8,71,63,559,496,4401,3905,34649,30744,272791,242047,2147679,
%T A177187 1905632,16908641,15003009,133121449,118118440,1048062951,929944511,
%U A177187 8251382159,7321437648,64962994321,57641556673,511452572409,453811015736,4026657584951,3572846569215
%N A177187 Union of A057080 and A001090.
%C A177187 Column sums of shifted Pascal-like array:
%C A177187   1..1..10..10..100..100.1000.1000
%C A177187   ......-1..-2..-30..-40.-500.-600
%C A177187   ................1....3...60..100
%C A177187   .........................-1...-4
%C A177187   -------------------------------- +
%C A177187   1..1...9...8...71...63..559..496
%C A177187 Decimal expansion of ratio n/(n+1) is accumulation of Catalan numbers; (5 +/- sqrt(15)).
%H A177187 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
%F A177187 For n odd a(n) = 10*a(n-1) - a(n-2), for n even a(n) = a(n-1) - a(n-2); with a(0) = 0, a(1) = 1.
%F A177187 G.f.: x*(1+x+x^2) / ( 1-8*x^2+x^4 ). - _R. J. Mathar_, Nov 11 2011
%Y A177187 Cf. A057080, A001090, A041059, A004189, A000108.
%Y A177187 Cf. A010472.
%K A177187 nonn,easy
%O A177187 1,3
%A A177187 _Mark Dols_, May 04 2010