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A332662
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Put-and-count: An enumeration of N X N where N = {0, 1, 2, ...}. The terms are interleaved x and y coordinates. Or: A row-wise storage scheme for sequences of regular triangles.
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7
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0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 1, 2, 1, 3, 0, 4, 0, 5, 0, 0, 3, 1, 2, 2, 2, 3, 1, 4, 1, 5, 1, 6, 0, 7, 0, 8, 0, 9, 0, 0, 4, 1, 3, 2, 3, 3, 2, 4, 2, 5, 2, 6, 1, 7, 1, 8, 1, 9, 1, 10, 0, 11, 0, 12, 0, 13, 0, 14, 0, 0, 5, 1, 4, 2, 4, 3, 3, 4, 3, 5, 3, 6, 2, 7, 2
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OFFSET
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0,7
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COMMENTS
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Other enumerations of N X N designed with storage allocation for extensible arrays in mind include A319514 and A319571.
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LINKS
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EXAMPLE
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Illustrating the linear storage layout of a sequence of regular triangles.
(A) [ 0], [ 2, 3], [ 7, 8, 9], [16, 17, 18, 19], [30, 31, 32, 33, 34], ...
(B) [ 1], [ 5, 6], [13, 14, 15], [26, 27, 28, 29], ...
(C) [ 4], [11, 12], [23, 24, 25], ...
(D) [10], [21, 22], ...
(E) [20], ...
...
The start values of all partial rows (in ascending order) are 0 plus A014370.
The start values of the partial rows in the first row are A005581 (without first 0).
The start values of the partial rows on the main diagonal are A331987.
The end values of all partial rows (in ascending order) are A332023.
The end values of the partial rows in the first row are A062748.
The end values of the partial rows on the main diagonal are A332698.
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MAPLE
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count := (k, A) -> ListTools:-Occurrences(k, A): t := n -> n*(n+1)/2:
PutAndCount := proc(N) local L, n, v, c, seq; L := NULL; seq := NULL;
for n from 1 to N do
for v from 0 to t(n)-1 do
# How often did you see v in this sequence before?
c := count(v, [seq]);
L := L, v, c; seq := seq, v;
od od; L end: PutAndCount(6);
# Returning 'seq' instead of 'L' gives the x-coordinates (A332663).
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PROG
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(Julia)
function a_list(N)
a = Int[]
for n in 1:N
i = 0
for j in ((k:-1:1) for k in 1:n)
t = n - j[1]
for m in j
push!(a, i, t)
i += 1
end end end; a end
a_list(5) |> println
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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