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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; initial terms are 0,1,4.
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%I #21 Feb 04 2025 18:08:54

%S 0,1,4,5,9,15,29,54,102,190,355,662,1236,2307,4307,8040,15009,28018,

%T 52303,97637,182265,340245,635156,1185684,2213388,4131865,7713202,

%U 14398700,26878923,50176509,93667520,174854817,326412048,609333085,1137478873,2123400515

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

%H Harvey P. Dale, <a href="/A049860/b049860.txt">Table of n, a(n) for n = 0..1000</a>

%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).

%F G.f.: (x+2*x^2-3*x^3)/(1-2*x+x^3-x^4). - _Harvey P. Dale_, Jun 15 2019

%t LinearRecurrence[{2,0,-1,1},{0,1,4,5},50] (* _Harvey P. Dale_, Jun 15 2019 *)

%K nonn,easy

%O 0,3

%A _Clark Kimberling_