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Search: id:A058195
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| A058195 |
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Areas of a sequence of right-angled figures described below. |
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+0
1
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| 1, 7, 23, 57, 118, 218, 370, 590, 895, 1305, 1841, 2527, 3388, 4452, 5748, 7308, 9165, 11355, 13915, 16885, 20306, 24222, 28678, 33722, 39403, 45773, 52885, 60795, 69560, 79240, 89896, 101592, 114393, 128367, 143583, 160113, 178030
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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From the NW corner to the SE corner, going the upper (or right) way, the edges have lengths n, n-1, ..., 2, 1, 1, 2, ..., n-1, n. Going the lower (or left) way, the edges have lengths n,1,n-1,2,...,2,n-1,1,n.
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FORMULA
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a(n) = [(2n^4+10n^3+13n^2+2n)/24], where [] denotes floor. (For even n there is no need for truncation. For odd n the [] removes 1/8.) A formula without [] is (4n^4+20n^3+26n^2+4n+3+3(-1)^(n+1))/48.
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EXAMPLE
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For n=6 the figure is (assuming the "#" character is square ...):
######
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##########
.#########
.#########
.###########
.############
.############
...#############
...#############
...#############
...#############
......###############
......###############
......###############
..........###########
..........###########
...............######
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CROSSREFS
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Adjacent sequences: A058192 A058193 A058194 this_sequence A058196 A058197 A058198
Sequence in context: A022815 A027116 A027918 this_sequence A037165 A126284 A140096
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KEYWORD
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easy,nonn
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AUTHOR
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Jonas Wallgren (jonwa(AT)ida.liu.se), Nov 26 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 06 2000
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