OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 18 2011
Also sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is one of the four semi-diagonals of the spiral. - Omar E. Pol, Oct 14 2011
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 10*n^2 - 5*n = A000384(n)*5.
a(n) = a(n-1) + 20*n-15 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
From G. C. Greubel, Sep 01 2018: (Start)
G.f.: 5*x*(1+ 3*x)/(1-x)^3.
E.g.f.: 5*x*(1+2*x)*exp(x). (End)
From Vaclav Kotesovec, Sep 02 2018: (Start)
Sum_{n>=1} 1/a(n) = 2*log(2)/5.
Sum_{n>=1} (-1)^n/a(n) = log(2)/5 - Pi/10. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 5, 30}, 50] (* or *) Table[5*n*(2*n-1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *)
PROG
(PARI) a(n)=5*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [5*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved