OFFSET
0,2
COMMENTS
20 times the n-th triangular number.
a(n) is the number of one-sided n-step prudent walks, from (0,0) to (3,3), for n-6 is even. - Shanzhen Gao, Apr 26 2011
Numbers k such that 10*k + 25 is a square. - Bruno Berselli, May 14 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..875
Shanzhen Gao and Keh-Hsun Chen, Tackling Sequences From Prudent Self-Avoiding Walks, FCS'14, The 2014 International Conference on Foundations of Computer Science.
Shanzhen Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: 20*x/(1-x)^3.
E.g.f.: 10*x*(x+2)*exp(x). - G. C. Greubel, Aug 03 2017
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/10.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/10.
Product_{n>=1} (1 - 1/a(n)) = -(10/Pi)*cos(sqrt(7/5)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (10/Pi)*cos(sqrt(3/5)*Pi/2). (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 20, 60}, 50] (* or *) Table[10*n*(n+1), {n, 0, 50}] (* G. C. Greubel, Aug 03 2017 *)
PROG
(Magma) [10*n*(n+1): n in [0..50]];
(PARI) a(n)=10*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 03 2009
EXTENSIONS
Entries checked by R. J. Mathar, Aug 06 2009
STATUS
approved