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a(n)=Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; 3 initial terms required.
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%I #14 Feb 19 2018 22:01:46

%S 2,3,4,7,13,25,47,88,164,306,571,1066,1990,3715,6935,12946,24167,

%T 45114,84217,157213,293479,547855,1022714,1909162,3563948,6653037,

%U 12419626,23184466,43279843,80793097,150821354,281547331,525581408

%N a(n)=Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; 3 initial terms required.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, 1).

%F a(n)=2*a(n-1)-a(n-3)+a(n-4); 4 initial terms required.

%t LinearRecurrence[{2 ,0,-1,1},{2,3,4,7},40] (* _Harvey P. Dale_, May 02 2012 *)

%K nonn

%O 0,1

%A _Clark Kimberling_