login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143859 Ulam's spiral (WNW spoke). 3

%I

%S 1,18,67,148,261,406,583,792,1033,1306,1611,1948,2317,2718,3151,3616,

%T 4113,4642,5203,5796,6421,7078,7767,8488,9241,10026,10843,11692,12573,

%U 13486,14431,15408,16417,17458,18531,19636,20773,21942,23143,24376

%N Ulam's spiral (WNW spoke).

%C Also sequence found by reading the segment (1, 18) together with the line from 18, in the direction 18, 67, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012

%H Harvey P. Dale, <a href="/A143859/b143859.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 16n^2-31n+16. - _R. J. Mathar_, Sep 08 2008

%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3), a(1)=1, a(2)=18, a(3)=67. - _Harvey P. Dale_, Mar 24 2012

%F G.f.: x*(1+15*x+16*x^2)/(1-x)^3. - _Colin Barker_, Aug 03 2012

%t f[n_] := 16n^2 -31n +16; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008 *)

%t LinearRecurrence[{3,-3,1},{1,18,67},40] (* _Harvey P. Dale_, Mar 24 2012 *)

%t CoefficientList[Series[(1 + 15 x + 16 x^2) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)

%o (MAGMA) [16*n^2-31*n+16: n in [1..50]]; // _Vincenzo Librandi_, Nov 08 2014

%o (PARI) vector(50, n, 16*n^2-31*n+16) \\ _Michel Marcus_, Nov 08 2014

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)