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, 11385, 11891

Offset: 0

Author

Omar E. Pol, Dec 12 2008

Keywords

• nonn
• easy

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 5*n to 6*n. - 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).

Crossrefs

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

Programs

Magma

[11*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015

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 *)

PARI

my(x='x+O('x^100)); concat(0, Vec(11*x/(1-x)^3)) \\ Altug Alkan, Dec 23 2015

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(11*n+10).

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

a(n) = Sum_{i=5*n..6*n} 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)

E.g.f.: 11*exp(x)*x*(2 + x)/2. - Elmo R. Oliveira, Dec 25 2024