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 A024873 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). 0

%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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Last modified September 21 17:55 EDT 2023. Contains 365503 sequences. (Running on oeis4.)