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%I #12 Jul 30 2015 22:11:05
%S 6,8,26,43,97,156,308,499,915,1480,2598,4204,7178,11614,19476,31513,
%T 52219,84492,138900,224745,367509,594642,968924,1567752,2548478,
%U 4123524,6692462,10828631,17556405,28406860,46023972,74468351,120596327,195128956,315902914
%N a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 2), t = (Lucas numbers).
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -2, -1, -1, -3, 2, 1, 1, 1).
%F G.f.:(-6+2*x^7+x^6+4*x^5+2*x^4-5*x^3-2*x)/((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]
%F a(0)=6, a(1)=8, a(2)=26, a(3)=43, a(4)=97, a(5)=156, a(6)=308, a(7)=499, a(8)=915, a(9)=1480, a(n)=a(n-1)+3*a(n-2)-2*a(n-3)-a(n-4)-a(n-5)- 3*a(n-6)+2*a(n-7)+a(n-8)+a(n-9)+a(n-10) [From Harvey P. Dale, May 19 2011]
%t LinearRecurrence[{1,3,-2,-1,-1,-3,2,1,1,1},{6,8,26,43,97,156,308, 499, 915,1480},50] (* or *) CoefficientList[ Series[ (-6+2x^7+x^6+4x^5+2x^4- 5x^3-2x)/((x^2+x-1)(x^4+x^2-1)^2),{x,0,50}],x] (* _Harvey P. Dale_, May 19 2011 *)
%K nonn
%O 2,1
%A _Clark Kimberling_
%E More terms from Harvey P. Dale, May 19 2011.
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