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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 square spiral.
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8
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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
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OFFSET
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0,2
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COMMENTS
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The 3 X 3 and 5 X 5 spirals are
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7---8---9
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6 1---2
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5---4---3
with 7+9+1+5+3=25
and
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21--22--23--24--25
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20 7---8---9--10
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19 6 1---2 11
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18 5---4---3 12
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17--16--15--14--13
with 21+25+7+9+1+5+3+17+13=101.
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 0..10000
Project Euler, Problem 28
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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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, Feb 10 2008
a(n) = 1 + 10*n^2 + (16*n^3 + 26*n)/3. [Corrected by Arie Groeneveld, Aug 17 2008]
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MATHEMATICA
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Array[1 + 10 #^2 + (16 #^3 + 26 #)/3 &, 36, 0] (* Michael De Vlieger, Mar 01 2018 *)
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PROG
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(PARI) a(n) = 1 + 10*n^2 + (16*n^3 + 26*n)/3; \\ Joerg Arndt, Mar 01 2018
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CROSSREFS
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Cf. A016754, A054569, A053755, A054554 for diagonals from origin.
Cf. A325958 (first differences).
Sequence in context: A356533 A221274 A042220 * A042222 A158551 A044276
Adjacent sequences: A114251 A114252 A114253 * 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, Feb 06 2008, Mar 01 2008
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STATUS
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approved
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