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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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G. C. Greubel, 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 - 27*n + 12, n>0. - R. J. Mathar, Sep 04 2008
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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f[n_]:= 16n^2 -27n +12; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *)
CoefficientList[Series[(1+19x+12x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
((32*Range[50]-27)^2 +39)/64 (* G. C. Greubel, Nov 09 2019 *)
LinearRecurrence[{3, -3, 1}, {1, 22, 75}, 40] (* Harvey P. Dale, Sep 26 2020 *)
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PROG
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(Magma) [16*n^2-27*n+12: n in [1..50]]; // Vincenzo Librandi, Nov 08 2014
(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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Sequence in context: A251286 A080861 A241521 * A282723 A003908 A075252
Adjacent sequences: A143835 A143836 A143837 * A143839 A143840 A143841
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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 02 2008
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STATUS
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approved
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