A022268 a(n) = n*(11*n - 1)/2.

0, 5, 21, 48, 86, 135, 195, 266, 348, 441, 545, 660, 786, 923, 1071, 1230, 1400, 1581, 1773, 1976, 2190, 2415, 2651, 2898, 3156, 3425, 3705, 3996, 4298, 4611, 4935, 5270, 5616, 5973, 6341, 6720, 7110, 7511, 7923, 8346, 8780, 9225, 9681, 10148, 10626, 11115

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of sets with two elements that can be obtained by selecting distinct elements from two sets with 2n and 3n elements respectively and n common elements. - Polina S. Dolmatova (polinasport(AT)mail.ru), Jul 11 2003

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, A022281.

Cf. index to sequence with numbers of the form n*(d*n+10-d)/2 in A140090.

Cf. similar sequences listed in A022288.

Programs

Magma

[n*(11*n - 1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 04 2016

Maple

A022268:=n->n*(11*n - 1)/2: seq(A022268(n), n=0..50); # Wesley Ivan Hurt, Dec 04 2016

Mathematica

Table[n (11 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 14 2016 *)

PARI

a(n)=n*(11*n-1)/2 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: x*(5 + 6*x)/(1-x)^3. - Bruno Berselli, Feb 11 2011

a(n) = 11*n + a(n-1) - 6 for n>0. - Vincenzo Librandi, Aug 04 2010

a(n) = A000217(6*n-1) - A000217(5*n-1). - Bruno Berselli, Oct 17 2016

From Wesley Ivan Hurt, Dec 04 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.

a(n) = (1/9) * Sum_{i=n..10n-1} i. (End)

E.g.f.: (1/2)*(11*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017