OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 11,... and the same line from 0, in the direction 0, 33,..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Axis perpendicular to A195149 in the same spiral. - Omar E. Pol, Sep 18 2011
Sum of the numbers from 5n to 6n. - Wesley Ivan Hurt, Dec 22 2015
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 11*n*(n+1)/2 = 11*A000217(n).
a(n) = a(n-1)+11*n with n>0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
a(n) = A069125(n+1) - 1. - Omar E. Pol, Oct 03 2011
From Philippe Deléham, Mar 27 2013: (Start)
G.f.: 11*x/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) for n>2, a(0)=0, a(1)=11, a(2)=33.
a(n) = A218530(11n+10).
a(n) = Sum_{i=5n..6n} i. - Wesley Ivan Hurt, Dec 22 2015
From Amiram Eldar, Feb 21 2023: (Start)
Sum_{n>=1} 1/a(n) = 2/11.
Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/11.
Product_{n>=1} (1 - 1/a(n)) = -(11/(2*Pi))*cos(sqrt(19/11)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (11/(2*Pi))*cos(sqrt(3/11)*Pi/2). (End)
MAPLE
MATHEMATICA
Table[11*n*(n - 1)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 11, 33}, 100] (* G. C. Greubel, Dec 22 2015 *)
PROG
(Magma) [11*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015
(PARI) my(x='x+O('x^100)); concat(0, Vec(11*x/(1-x)^3)) \\ Altug Alkan, Dec 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved