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A143855
Ulam's spiral (ESE spoke).
4
1, 10, 51, 124, 229, 366, 535, 736, 969, 1234, 1531, 1860, 2221, 2614, 3039, 3496, 3985, 4506, 5059, 5644, 6261, 6910, 7591, 8304, 9049, 9826, 10635, 11476, 12349, 13254, 14191, 15160, 16161, 17194, 18259, 19356, 20485, 21646, 22839, 24064
OFFSET
1,2
COMMENTS
Also sequence found by reading the segment (1, 10) together with the line from 10, in the direction 10, 51, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
FORMULA
a(n) = 16*n^2 - 39*n + 24. - R. J. Mathar, Sep 08 2008
G.f.: x*(1 + 7*x + 24*x^2)/(1-x)^3. - Colin Barker, Aug 03 2012
E.g.f.: -24 + (24 - 23*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
MAPLE
seq( ((32*n -39)^2 +15)/64, n=1..50); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_]:= 16n^2 -39n +24; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 04 2008 *)
CoefficientList[Series[(1+7x+24x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
((32*Range[50] -39)^2 +15)/64 (* G. C. Greubel, Nov 09 2019 *)
PROG
(Magma) [16*n^2-39*n+24: n in [1..50]]; // Vincenzo Librandi, Nov 08 2014
(PARI) vector(50, n, 16*n^2-39*n+24) \\ Michel Marcus, Nov 08 2014
(Sage) [((32*n-39)^2 +15)/64 for n in (1..50)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..50], n-> ((32*n-39)^2 +15)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
Sequence in context: A106041 A370737 A264044 * A124162 A077044 A069038
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 03 2008, Sep 04 2008
STATUS
approved