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A137928
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The even principal diagonal of an 2nX2n spiral.
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4
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2, 4, 10, 16, 26, 36, 50, 64, 82, 100, 122, 144, 170, 196, 226, 256, 290, 324, 362, 400, 442, 484, 530, 576, 626, 676, 730, 784, 842, 900, 962, 1024, 1090, 1156, 1226, 1296, 1370, 1444, 1522, 1600, 1682, 1764, 1850, 1936, 2026, 2116, 2210, 2304, 2402, 2500, 2602, 2704, 2810
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
a(n) = A171218(n) - A171218(n-1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 05 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,1)
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FORMULA
| a(n) = 2n + 4*floor((n-1)^2/4) = 2n + 4*A002620(n-1).
G.f. -2*x*(1+x^2) / ( (1+x)*(x-1)^3 ). a(n) = 2*A000982(n). - R. J. Mathar, Jun 27 2011
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EXAMPLE
| a(1) = 2(1) + 4*floor((1-1)/4) = 2
a(2) = 2(2) + 4*floor((2-1)/4) = 4
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PROG
| (Python) a = lambda n: 2*n + 4*floor((n-1)**2/4)
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CROSSREFS
| Cf. A002061 (odd diagonal), A002620.
Sequence in context: A189558 A111149 A123689 * A144834 A006584 A032246
Adjacent sequences: A137925 A137926 A137927 * A137929 A137930 A137931
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KEYWORD
| nonn,easy
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AUTHOR
| William A. Tedeschi (fynmun(AT)hotmail.com), Feb 29 2008
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