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%I #17 Oct 11 2019 07:50:56
%S 1,4,5,8,9,12,13,16,19,20,23,24,27,28,31,32,35,36,39,40,43,46,47,50,
%T 51,54,55,58,59,62,63,66,69,70,73,74,77,78,81,82,85,86,89,90,93,96,97,
%U 100,101,104,105,108,111,112,115,116,119,120,123,124,127
%N Compound sequence with a(n) = A319198(A278040(n)), for n >= 0.
%C Old name was: Compound tribonacci sequence a(n) = A319198(A278040(n)), for n >= 0.
%C a(n) gives the sum of the entries of the tribonacci word sequence t = A080843 not exceeding t(A(n)), with A(n) = A278040(n).
%F a(n) = z(A(n)) = Sum_{j=0..A(n)} t(j), n >= 0, with z = A319198, A = A278040 and t = A080843.
%F a(n) = 2*(A(n) - B(n)) - (n + 1), where B(n) = A278039(n). For a proof see the W. Lang link in A080843, Proposition 8, eq. (45).
%F a(n)= 1 + Sum_{k=1..n-1} d(k), where d is the tribonacci sequence on the alphabet {3,1,1}. - _Michel Dekking_, Oct 08 2019
%e n = 4, A(4) = 14, t = {0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, ...}, which sums to 9 = a(4) = 2*(14 - 7) - 5, because B(4) = 7.
%Y Cf. A080843, A278040, A278039, A319198, A322407, A322408.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Dec 27 2018
%E Name changed by _Michel Dekking_, Oct 08 2019
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