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A237718 9-distance Pell numbers.

%I A237718 #34 May 01 2017 03:01:53
%S A237718 1,1,1,1,1,1,1,1,1,3,3,5,5,7,7,9,9,11,15,17,25,27,39,41,57,59,79,89,
%T A237718 113,139,167,217,249,331,367,489,545,715,823,1049,1257,1547,1919,2281,
%U A237718 2897,3371,4327,5017,6425,7531,9519
%N A237718 9-distance Pell numbers.
%H A237718 G. C. Greubel, <a href="/A237718/b237718.txt">Table of n, a(n) for n = 0..1000</a>
%H A237718 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,0,0,2).
%F A237718 a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=1, a(8)=1; a(n) = 2*a(n-9) + a(n-2) for n>=9.
%F A237718 G.f. (1+x)/(1-x^2-2x^9).
%F A237718 a(2*n) = Sum_{j=0..n/9} Binomial[n-7j, 2j]*2^{2j} + Sum_{j=0..(n-5)/9} Binomial[n-4-7j, 2j+1]*2^{2j+1}.
%F A237718 a(2*n+1) = Sum_{j=0..n/9} Binomial[n-7j, 2j]*2^{2j} + Sum_{j=0..(n-4)/9} Binomial[n-3-7j, 2j+1]*2^{2j+1}.
%e A237718 a(9)=2a(0)+a(7)=3; a(10)=2a(1)+a(8)=3; a(11)=2a(2)+a(9)=5.
%t A237718 For[j = 0, j < 9, j++, a[j] = 1]
%t A237718 For[j = 9, j < 51, j++, a[j] = 2 a[j - 9] + a[j - 2]]
%t A237718 Table[a[j], {j, 0, 50}]
%t A237718 CoefficientList[Series[(1 + x)/(1 - x^2 - 2 x^9), {x,0,50}], x] (* _G. C. Greubel_, May 01 2017 *)
%o A237718 (PARI) Vec((1+x)/(1-x^2-2*x^9)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 06 2014
%Y A237718 Cf. A000129, A122522, A159284, A237714, A237716, A237717.
%K A237718 nonn,easy
%O A237718 0,10
%A A237718 _Sergio Falcon_, Feb 12 2014