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Search: id:A114254
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| A114254 |
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Sum of all terms on the two principal diagonals of a 2n+1 X 2n+1 ssquare spiral. |
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+0
2
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| 1, 25, 101, 261, 537, 961, 1565, 2381, 3441, 4777, 6421, 8405, 10761, 13521, 16717, 20381, 24545, 29241, 34501, 40357, 46841, 53985, 61821, 70381, 79697, 89801, 100725, 112501, 125161, 138737, 153261, 168765, 185281, 202841, 221477, 241221
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The 3 X 3 and 5 X 5 spirals are
7 8 9
6 1 2
5 4 3
and
21..22..23..24..25
20..7...8...9...10
19..6...1...2...11
18..5...4...3...12
17..16..15..14..13
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FORMULA
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O.g.f.: 3/(-1+x)+16/(-1+x)^2+44/(-1+x)^3+32/(-1+x)^4 = (1+21*x+7*x^2+3*x^3)/(-1+x)^4 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2008
a(n) = 1 + 10*n^2 + [(16n^3 + 26n)/3]. [Corrected by Arie Groeneveld (bradypus(at)xs4all.nl), Aug 17 2008]
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PROGRAM
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Python:
.l = input("Length of Diagonal? ")
.Sigma = 1 + 4*sum(4*k**2+k+3-2*((k+2)%(k+1)) for k in range(1, l+1))
.print Sigma
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CROSSREFS
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Cf. A016754, A054569, A053755, A054554 for diagonals from origin.
Cf. A011655.
Sequence in context: A134422 A016850 A042220 this_sequence A042222 A158551 A044276
Adjacent sequences: A114251 A114252 A114253 this_sequence A114255 A114256 A114257
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KEYWORD
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easy,nonn
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AUTHOR
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William A. Tedeschi (fynmun(AT)hotmail.com), Feb 06 2008, Mar 01 2008
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