A180223 a(n) = (11*n^2 - 7*n)/2.

0, 2, 15, 39, 74, 120, 177, 245, 324, 414, 515, 627, 750, 884, 1029, 1185, 1352, 1530, 1719, 1919, 2130, 2352, 2585, 2829, 3084, 3350, 3627, 3915, 4214, 4524, 4845, 5177, 5520, 5874, 6239, 6615, 7002, 7400, 7809, 8229, 8660

Offset: 0

Author

Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010

Keywords

• nonn
• easy

Comments

This sequence is related to A050441 by n*a(n) - Sum_{i=0..n-1} a(i) = 2*A050441(n). - Bruno Berselli, Aug 19 2010

Sum of n-th heptagonal number (A000566) and n-th octagonal number (A000567). - Bruno Berselli, Jun 11 2013

Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - J. M. Bergot, Jun 17 2013

Links

• B. Berselli, Table of n, a(n) for n = 0..10000.
• B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A050441, A000566, A000567, A226492.

Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=11). - Bruno Berselli, Jun 10 2013

Programs

GAP

List([0..30], n-> n*(11*n-7)/2); # G. C. Greubel, Sep 18 2019

Magma

[(11*n^2 - 7*n)/2: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

Maple

A180223:=n->(11*n^2 - 7*n)/2; seq(A180223(n), n=0..30); # Wesley Ivan Hurt, Feb 25 2014

Mathematica

Table[(11*n^2 - 7*n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Feb 25 2014 *)
LinearRecurrence[{3,-3,1},{0,2,15},50] (* Harvey P. Dale, Oct 10 2020 *)

PARI

a(n)=1/2*(11*n^2 - 7*n);

Sage

[n*(11*n-7)/2 for n in (0..30)] # G. C. Greubel, Sep 18 2019

Formula

G.f.: x*(2+9*x)/(1-x)^3. - Bruno Berselli, Aug 19 2010 - corrected in Apr 18 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with n>2. - Bruno Berselli, Aug 19 2010

a(n) = n + A226492(n). - Bruno Berselli, Jun 11 2013

E.g.f.: x*(4 + 11*x)*exp(x)/2. - G. C. Greubel, Aug 24 2015