A186029 a(n) = n*(7*n+3)/2.

0, 5, 17, 36, 62, 95, 135, 182, 236, 297, 365, 440, 522, 611, 707, 810, 920, 1037, 1161, 1292, 1430, 1575, 1727, 1886, 2052, 2225, 2405, 2592, 2786, 2987, 3195, 3410, 3632, 3861, 4097, 4340, 4590, 4847, 5111, 5382, 5660, 5945, 6237, 6536, 6842, 7155, 7475

Offset: 0

Author

Bruno Berselli, Feb 11 2011

Keywords

• nonn
• easy

Comments

This sequence is related to A050409 by A050409(n) = n*a(n) - Sum_{i=0..n-1} a(i).

Examples

			From _Ilya Gutkovskiy_, Mar 31 2016: (Start)
.                                           o o o o o o o o o o o o
.                                           o                     o
.         o o o o o o   o  o o o o o o  o   o  o  o o o o o o  o  o
.         o         o   o  o         o  o   o  o  o         o  o  o
. o   o   o  o   o  o   o  o  o   o  o  o   o  o  o  o   o  o  o  o
. o o o   o  o o o  o   o  o  o o o  o  o   o  o  o  o o o  o  o  o
.                       o               o   o  o               o  o
.                       o o o o o o o o o   o  o o o o o o o o o  o
.
.  n=1        n=2              n=3                    n=4
(End)
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. numbers of the form n*(d*n+10-d)/2 indexed in A140090.

Cf. A017041 (first differences).

Cf. A001106, A022264, A022265, A024966, A050409, A067727, A174738, A179986, A218471.

Programs

Magma

[n*(7*n+3)/2: n in [0..44]];

Mathematica

Table[(n - 1) (7 n - 4)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
LinearRecurrence[{3,-3,1},{0,5,17},50] (* Harvey P. Dale, Sep 07 2022 *)

PARI

a(n)=n*(7*n+3)/2 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: x*(5+2*x)/(1-x)^3.

a(n) - a(-n) = A008585(n).

a(n) + a(-n) = A033582(n).

n*a(n+1) - (n+1)*a(n) = A024966(n). - Bruno Berselli, May 30 2012

n*a(n+2) - (n+2)*a(n) = A067727(n) for n>0. - Bruno Berselli, May 30 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=17. - Philippe Deléham, Mar 26 2013

a(n) = A174738(7*n+4). - Philippe Deléham, Mar 26 2013

E.g.f.: (1/2)*(7*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017