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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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.
Empirical G.f.: x*(1+7*x-3*x^2+3*x^3)/((1-x)^4*(1+x)). [Colin Barker, Jan 12 2012]
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EXAMPLE
| 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
| Cf. A114254, A137931.
Sequence in context: A022670 A072277 A063424 * A071289 A156183 A124870
Adjacent sequences: A137927 A137928 A137929 * A137931 A137932 A137933
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KEYWORD
| nonn
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AUTHOR
| William A. Tedeschi (fynmun(AT)hotmail.com), Feb 29 2008
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