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A143854
Ulam's spiral (WSW spoke).
4
1, 20, 71, 154, 269, 416, 595, 806, 1049, 1324, 1631, 1970, 2341, 2744, 3179, 3646, 4145, 4676, 5239, 5834, 6461, 7120, 7811, 8534, 9289, 10076, 10895, 11746, 12629, 13544, 14491, 15470, 16481, 17524, 18599, 19706, 20845, 22016, 23219, 24454
OFFSET
1,2
COMMENTS
Also sequence found by reading the segment (1, 20) together with the line from 20, in the direction 20, 71, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
FORMULA
From Colin Barker, Aug 03 2012: (Start)
a(n) = 14 - 29*n + 16*n^2.
G.f.: x*(1 + 17*x + 14*x^2)/(1-x)^3. (End)
E.g.f.: -14 + (14 - 13*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
MAPLE
seq( ((32*n-29)^2 +55)/64, n=1..40); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_]:= 16n^2 -29n +14; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 03 2008 *)
CoefficientList[Series[(1+17x+14x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
((32*Range[50] -29)^2 +55)/64 (* G. C. Greubel, Nov 09 2019 *)
PROG
(Magma) [14-29*n+16*n^2: n in [1..50]]; // Vincenzo Librandi, Nov 08 2014
(PARI) vector(50, n, 14-29*n+16*n^2) \\ Michel Marcus, Nov 08 2014
(Sage) [((32*n-29)^2 +55)/64 for n in (1..50)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..50], n-> ((32*n-29)^2 +55)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
Sequence in context: A052516 A083873 A240820 * A263969 A139241 A139232
KEYWORD
nonn,easy
AUTHOR
STATUS
approved