A143855 Ulam's spiral (ESE spoke).

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Adjacent sequences: A143852 A143853 A143854 * A143856 A143857 A143858

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 03 2008, Sep 04 2008

Status

approved