OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 11, ..., and the line from 3, in the direction 3, 24, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. - Omar E. Pol, Sep 26 2011
For n >= 3, a(n) is the sum of the numbers appearing in the 3rd row of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 17 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
A. Horzela, P. Blasiak, G. E. H. Duchamp, K. A. Penson and A. I. Solomon, A product formula and combinatorial field theory, arXiv:quant-ph/0409152, 2004.
Leo Tavares, Illustration: Hexagonal Trapeziums.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A110449(n, 2) for n>1.
a(n) = a(n-1) + 5*n - 2 for n>0, a(0)=0. - Vincenzo Librandi, Nov 18 2010
a(n) = A130520(5*n+2). - Philippe Deléham, Mar 26 2013
a(n) = A202803(n)/2. - Philippe Deléham, Mar 27 2013
From G. C. Greubel, Aug 23 2017: (Start)
G.f.: x*(2*x + 3)/(1-x)^3.
E.g.f.: (x/2)*(5*x+6)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 10+2*gamma+2*Psi(1/5) = 0.57635... see A001620 and A200135. - R. J. Mathar, May 30 2022
Sum_{n>=1} 1/a(n) = 10 - sqrt(1+2/sqrt(5))*Pi - sqrt(5)*log(phi) - 5*log(5)/2, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 10 2022
MAPLE
seq(binomial(5*n+1, 2)/5, n=0..34); # Zerinvary Lajos, Jan 21 2007
a:=n->sum(2*n+j, j=1..n): seq(a(n), n=0..38); # Zerinvary Lajos, Apr 29 2007
MATHEMATICA
Table[n (5 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)
PROG
(PARI) a(n)=n*(5*n+1)/2; \\ Joerg Arndt, Mar 27 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Incorrect comment deleted and minor errors corrected by Johannes W. Meijer, Feb 04 2010
STATUS
approved