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A349803 a(3*n) = 1 + 4*n^2, a(1+3*n) = 2 + 4*n*(n+1), a(2+3*n) = 5 + 4*n*(n+1).

%I A349803 #25 Jan 19 2022 13:51:47
%S A349803 1,2,5,5,10,13,17,26,29,37,50,53,65,82,85,101,122,125,145,170,173,197,
%T A349803 226,229,257,290,293,325,362,365,401,442,445,485,530,533,577,626,629,
%U A349803 677,730,733,785,842,845,901,962
%N A349803 a(3*n) = 1 + 4*n^2, a(1+3*n) = 2 + 4*n*(n+1), a(2+3*n) = 5 + 4*n*(n+1).
%C A349803 A261327 sorted in nondecreasing order.
%H A349803 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F A349803 a(-n) = a(n) - A099838(n+2).
%F A349803 a(n) = a(n-3)  +  4*A004523(n-1) for n >=  3
%F A349803      = a(n-6)  +  8*A004396(n-3) for n >=  6
%F A349803      = a(n-9)  + 12*A004523(n-4) for n >=  9
%F A349803      = a(n-12) + 16*A004396(n-6) for n >= 12
%F A349803      ...
%t A349803 nterms=100;LinearRecurrence[{1,0,2,-2,0,-1,1},{1,2,5,5,10,13,17},nterms] (* _Paolo Xausa_, Dec 01 2021 *)
%Y A349803 Cf. A261327.
%Y A349803 Trisections: A053755, A069894, A078370.
%Y A349803 Cf. A004396, A004523, A099838.
%K A349803 nonn,easy
%O A349803 0,2
%A A349803 _Paul Curtz_, Dec 01 2021