A152740 11 times triangular numbers.

0, 11, 33, 66, 110, 165, 231, 308, 396, 495, 605, 726, 858, 1001, 1155, 1320, 1496, 1683, 1881, 2090, 2310, 2541, 2783, 3036, 3300, 3575, 3861, 4158, 4466, 4785, 5115, 5456, 5808, 6171, 6545, 6930, 7326, 7733, 8151, 8580, 9020, 9471, 9933, 10406, 10890

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) = A211013(n)+n = A022269(n)+5n = A022268(n)+6n = A180223(n)+9n = A051865(n)+10n. (End)

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

A152740:=n->11*n*(n+1)/2: seq(A152740(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015

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

Cf. A000217, A022268, A022269, A049598, A051865, A069125, A124080, A180223, A195149, A195313, A211013, A218530.

Sequence in context: A132285 A249166 A296543 * A080859 A063036 A163673

Adjacent sequences: A152737 A152738 A152739 * A152741 A152742 A152743

Keyword

nonn,easy

Author

Omar E. Pol, Dec 12 2008

Status

approved