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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 (list; graph; refs; listen; history; text; internal format)
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

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 - 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 *)

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

Adjacent sequences:  A143835 A143836 A143837 * A143839 A143840 A143841

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 02 2008

STATUS

approved

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Last modified April 9 01:33 EDT 2020. Contains 333339 sequences. (Running on oeis4.)