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A220464 Reverse reluctant sequence of reluctant sequence A002260.

%I A220464 #22 Feb 16 2022 11:59:19
%S A220464 1,1,1,2,1,1,1,2,1,1,2,1,2,1,1,3,2,1,2,1,1,1,3,2,1,2,1,1,2,1,3,2,1,2,
%T A220464 1,1,3,2,1,3,2,1,2,1,1,4,3,2,1,3,2,1,2,1,1,1,4,3,2,1,3,2,1,2,1,1,2,1,
%U A220464 4,3,2,1,3,2,1,2,1,1,3,2,1,4,3,2,1,3,2,1,2,1,1,4,3,2,1,4,3,2,1,3,2,1,2,1,1,5,4,3,2,1,4,3,2,1,3,2,1,2,1,1,1,5,4,3
%N A220464 Reverse reluctant sequence of reluctant sequence A002260.
%C A220464 Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.
%C A220464 Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
%C A220464 Sequence A002260 is the reluctant sequence of sequence 1,2,3,... (A000027).
%H A220464 Boris Putievskiy, <a href="/A220464/b220464.txt">Rows n = 1..140 of triangle, flattened</a>
%H A220464 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A220464 T(n,k) = A002260(n-k+1).
%F A220464 As a linear array, the sequence is a(n) = n1-t1*(t1+1)/2, where n1=(t*t+3*t+4)/2-n, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].
%e A220464 The start of the sequence as triangle array T(n,k) is:
%e A220464   1;
%e A220464   1,1;
%e A220464   2,1,1;
%e A220464   1,2,1,1;
%e A220464   2,1,2,1,1;
%e A220464   3,2,1,2,1,1;
%e A220464   ...
%o A220464 (Python)
%o A220464 t=int((math.sqrt(8*n-7) - 1)/ 2)
%o A220464 n1=(t*t+3*t+4)/2-n
%o A220464 t1=int((math.sqrt(8*n1-7) - 1)/ 2)
%o A220464 m=n1-t1*(t1+1)/2
%Y A220464 Cf. A002260, A004736, A220280.
%K A220464 easy,nonn,tabl
%O A220464 1,4
%A A220464 _Boris Putievskiy_, Dec 15 2012