cp's OEIS Frontend

A064766 Fill up an infinite triangular array by rows by successively writing numbers 1, then 1 up to 2*3/2, then 1 up to 3*4/2, then 1 up to 4*5/2 and so on, at the k-th step writing the numbers from 1 up to the k-th triangular number. The final elements of the rows of this infinite triangle form the sequence.

%I A064766 #23 Nov 01 2024 14:59:28
%S A064766 1,2,2,6,5,1,8,1,10,20,10,22,7,21,36,16,33,6,25,45,11,33,56,14,39,65,
%T A064766 14,42,71,10,41,73,1,35,70,106,23,61,100,4,45,87,130,21,66,112,159,36,
%U A064766 85,135,186,48,101,155,210,56,113,171,230,59,120,182,245,56,121,187
%N A064766 Fill up an infinite triangular array by rows by successively writing numbers 1, then 1 up to 2*3/2, then 1 up to 3*4/2, then 1 up to 4*5/2 and so on, at the k-th step writing the numbers from 1 up to the k-th triangular number. The final elements of the rows of this infinite triangle form the sequence.
%C A064766 An alternative, equivalent, definition: Let T(i) = [1,2,3,...,i*(i+1)/2], and let S be the concatenation of T(1), T(2), ... Create a triangle by partitioning S into rows of lengths 1, 2, 3, ... The right-hand elements of the rows of this triangle form the new sequence.
%H A064766 Harvey P. Dale, <a href="/A064766/b064766.txt">Table of n, a(n) for n = 0..1000</a>
%e A064766 The first few stages in the construction of the triangular array are:
%e A064766 1
%e A064766 then
%e A064766 ..1
%e A064766 .1.2.
%e A064766 3
%e A064766 then
%e A064766 ...1
%e A064766 ..1.2
%e A064766 .3.1.2
%e A064766 3.4.5.6
%e A064766 then
%e A064766 .....1
%e A064766 ....1.2
%e A064766 ...3.1.2
%e A064766 ..3.4.5.6
%e A064766 .1.2.3.4.5
%e A064766 6.7.8.9.10.
%e A064766 The right-most diagonal forms the sequence: 1,2,2,6,5,...
%t A064766 With[{nn=75},TakeList[Flatten[Range[1,#]&/@Accumulate[Range[nn]]],Range[nn]][[;;,-1]]] (* _Harvey P. Dale_, Oct 31 2024 *)
%Y A064766 Mini-index to these sequences: A064766, A064865, A064866, A065221-A655234 are all of the same type. See A064766 for a detailed explanation.
%K A064766 easy,nonn
%O A064766 0,2
%A A064766 _Floor van Lamoen_, Oct 18 2001
%E A064766 Edtied by _N. J. A. Sloane_, Oct 31 2024