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A143856
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Ulam's spiral (ENE spoke).
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4
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1, 12, 55, 130, 237, 376, 547, 750, 985, 1252, 1551, 1882, 2245, 2640, 3067, 3526, 4017, 4540, 5095, 5682, 6301, 6952, 7635, 8350, 9097, 9876, 10687, 11530, 12405, 13312, 14251, 15222, 16225, 17260, 18327, 19426, 20557, 21720, 22915, 24142
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OFFSET
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1,2
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COMMENTS
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Also sequence found by reading the segment (1, 12) together with the line from 12, in the direction 12, 55,..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 16*n^2 - 37*n + 22. - R. J. Mathar, Sep 08 2008
G.f. x*(1 + 9*x + 22*x^2)/(1-x)^3. - R. J. Mathar, Oct 31 2011
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 10 2012
E.g.f.: -22 + (22 - 21*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
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MAPLE
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seq( ((32*n-37)^2 +39)/64, n=1..40); # G. C. Greubel, Nov 09 2019
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MATHEMATICA
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f[n_]:= 16n^2 -37n +22; Array[f, 40] (* Robert G. Wilson v, Oct 31 2011 *)
Table[16n^2-37*n+22, {n, 1, 40}] (* Vincenzo Librandi, Jul 10 2012 *)
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PROG
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(Magma) [16*n^2 -37*n +22: n in [1..40]]; // Vincenzo Librandi, Jul 10 2012
(PARI) a(n)=16*n^2-37*n+22 \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [((32*n-37)^2 +39)/64 for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..40], n-> ((32*n-37)^2 +39)/64); # G. C. Greubel, Nov 09 2019
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CROSSREFS
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Sequence in context: A230920 A190948 A275249 * A207102 A343539 A229424
Adjacent sequences: A143853 A143854 A143855 * A143857 A143858 A143859
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Sep 03 2008
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STATUS
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approved
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