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Search: id:A137930
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| A137930 |
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The sum of the principal diagonals of an n X n spiral. |
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+0
2
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| 0, 1, 10, 25, 56, 101, 170, 261, 384, 537, 730, 961, 1240, 1565, 1946, 2381, 2880, 3441, 4074, 4777, 5560, 6421, 7370, 8405, 9536, 10761, 12090, 13521, 15064, 16717, 18490, 20381, 22400, 24545, 26826, 29241, 31800, 34501, 37354, 40357, 43520, 46841, 50330
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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n X n spirals of the form:
(Examples of n = 3, 4)
7...8...9
6...1...2
5...4...3
and
7...8...9...10
6...1...2...11
5...4...3...12
16..15..14..13
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FORMULA
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a(n) = mod(n^(n+1),n+1) + floor(n/2)^2*(6-4(-1)^n) + [16*floor(n/2)^3 + floor(n/2)*(14-12(-1)^n)]/3
Interweave A114254 and A137931.
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EXAMPLE
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a(1) = mod(1^(1+1),1+1) + floor(1/2)^2*(6-4(-1)^1) + [16*floor(1/2)^3 + floor(1/2)*(14-12(-1)^1)]/3 = 1
a(2) = mod(2^(2+1),2+1) + floor(2/2)^2*(6-4(-1)^2) + [16*floor(2/2)^3 + floor(2/2)*(14-12(-1)^2)]/3 = 10
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CROSSREFS
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Cf. A114254, A137931.
Sequence in context: A022670 A072277 A063424 this_sequence A071289 A124870 A078257
Adjacent sequences: A137927 A137928 A137929 this_sequence A137931 A137932 A137933
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KEYWORD
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nonn
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AUTHOR
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William A. Tedeschi (fynmun(AT)hotmail.com), Feb 29 2008
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