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A143838
Ulam's spiral (SSW spoke).
4
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
OFFSET
1,2
COMMENTS
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
FORMULA
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
MAPLE
seq( ((32*n-27)^2 +39)/64, n=1..50); # G. C. Greubel, Nov 09 2019
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A251286 A080861 A241521 * A282723 A003908 A075252
KEYWORD
nonn,easy
AUTHOR
STATUS
approved