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A143838
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Ulam's spiral (SSW spoke).
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4
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1, 22, 75, 160, 277, 426, 607, 820, 1065, 1342, 1651, 1992, 2365, 2770, 3207, 3676, 4177, 4710, 5275, 5872, 6501, 7162, 7855, 8580, 9337, 10126, 10947, 11800, 12685, 13602, 14551, 15532, 16545, 17590, 18667, 19776, 20917, 22090, 23295, 24532
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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, 22) together with the line from 22, in the direction 22, 75, ..., 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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FORMULA
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G.f.: x*(1 + 19*x + 12*x^2)/(1-x)^3. - Colin Barker, Aug 03 2012
E.g.f.: -12 + (12 - 11*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
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MAPLE
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seq( ((32*n-27)^2 +39)/64, n=1..50); # G. C. Greubel, Nov 09 2019
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MATHEMATICA
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CoefficientList[Series[(1+19x+12x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
LinearRecurrence[{3, -3, 1}, {1, 22, 75}, 40] (* Harvey P. Dale, Sep 26 2020 *)
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PROG
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(PARI) vector(50, n, 16*n^2-27*n+12) \\ Michel Marcus, Nov 08 2014
(Sage) [((32*n-27)^2 +39)/64 for n in (1..50)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..50], n-> ((32*n-27)^2 +39)/64); # G. C. Greubel, Nov 09 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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