OFFSET
0,2
COMMENTS
Sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the diagonals in the spiral. - Omar E. Pol, Sep 10 2011
Also sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is a line perpendicular to the main axis A195015 in the same spiral. - Omar E. Pol, Oct 14 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Leo Tavares, Illustration: Stellar Layers.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Reinhard Zumkeller, Mar 13 2009: (Start)
a(n) = a(n-1) + 20*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 17 2010
From G. C. Greubel, Oct 12 2019: (Start)
G.f.: (1 + 15*x + 4*x^2)/(1-x)^3.
E.g.f.: (1 + 17*x + 10*x^2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = sqrt(1+2/sqrt(5))*Pi/6 + sqrt(5)*log(phi)/6 + 5*log(5)/12 - 2*log(2)/3, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2022
From Elmo R. Oliveira, Dec 17 2025: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
MAPLE
seq((2*n+1)*(5*n+1), n=0..50); # G. C. Greubel, Oct 12 2019
MATHEMATICA
Table[(2*n+1)*(5*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
PROG
(PARI) a(n)=(2*n+1)*(5*n+1) \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(2*n+1)*(5*n+1): n in [0..50]]; // G. C. Greubel, Oct 12 2019
(SageMath) [(2*n+1)*(5*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n+1)*(5*n+1)); # G. C. Greubel, Oct 12 2019
CROSSREFS
Cf. A153127. - Reinhard Zumkeller, Dec 20 2008
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Terms a(36) onward added by G. C. Greubel, Oct 12 2019
STATUS
approved