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Search: id:A137931
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| A137931 |
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Sum of the principal diagonals of a 2n X 2n spiral. |
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+0
2
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| 0, 10, 56, 170, 384, 730, 1240, 1946, 2880, 4074, 5560, 7370, 9536, 12090, 15064, 18490, 22400, 26826, 31800, 37354, 43520, 50330, 57816, 66010, 74944, 84650, 95160, 106506, 118720, 131834, 145880, 160890, 176896, 193930, 212024, 231210, 251520, 272986, 295640
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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2nX2n spirals of the form:
(Example of n = 2)
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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f(n) = -1 + n + Sum{k=0..2n, 2k^2-k+1}
a(n) = 2n^2 + 2n + (16n^3 + 2n)/3
G.f.:(2*x*(3*x+5)*(x+1))/(x-1)^4 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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EXAMPLE
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a(0) = 2(0)^2 + 2(0) + (16(0)^3 + 2(0))/3 = 0
a(2) = 2(2)^2 + 2(2) + (16(2)^3 + 2(2))/3 = 56
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PROGRAM
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(Python) f = lambda n: -1 + n + sum(2*k**2 - k + 1 for k in range(0, 2*n+1))
(Python) a = lambda n: 2*n**2 + 2*n + (16*n**3 + 2*n)/3
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CROSSREFS
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Cf. A137928, A002061. A bisection of A137930.
Sequence in context: A001557 A164951 A000814 this_sequence A053493 A001786 A053309
Adjacent sequences: A137928 A137929 A137930 this_sequence A137932 A137933 A137934
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KEYWORD
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nonn,easy
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AUTHOR
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William A. Tedeschi (fynmun(AT)hotmail.com), Feb 29 2008
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