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A007401
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Add n-1 to n-th term of 'n appears n times' sequence (A002024).
(Formerly M2316)
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45
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1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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As a triangle: (1; 3,4; 6,7,8; 10,11,12,13; ...), Row sums = A127736: (1, 7, 21, 46, 85, 141, 217, ...). - Gary W. Adamson, Oct 25 2007
T(n,k) = ((n+k)^2+n-k)/2 - 1, n,k > 0, read by antidiagonals. - Boris Putievskiy, Jan 14 2013
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = ((t+2)^2 + i - j)/2-1, where
i = n-t*(t+1)/2,
j = (t*t+3*t+4)/2-n,
t = floor((-1+sqrt(8*n-7))/2). (End)
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EXAMPLE
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The start of the sequence as table:
1, 3, 6, 10, 15, 21, 28, ...
4, 7, 11, 16, 22, 29, 37, ...
8, 12, 17, 23, 30, 38, 47, ...
13, 18, 24, 31, 39, 48, 58, ...
19, 25, 32, 40, 49, 59, 70, ...
26, 33, 41, 50, 60, 71, 83, ...
34, 42, 51, 61, 72, 84, 97, ...
...
The start of the sequence as triangle array read by rows:
1;
3, 4;
6, 7, 8;
10, 11, 12, 13;
15, 16, 17, 18, 19;
21, 22, 23, 24, 25, 26;
28, 29, 30, 31, 32, 33, 34;
...
Row number r contains r numbers r*(r+1)/2, r*(r+1)/2+1, ..., r*(r+1)/2+r-1. (End)
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MATHEMATICA
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PROG
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(Haskell)
a007401 n = a007401_list !! n
a007701_list = [x | x <- [0..], a023531 x == 0]
(Python)
from math import isqrt
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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