A022272 a(n) = n*(15*n - 1)/2.

0, 7, 29, 66, 118, 185, 267, 364, 476, 603, 745, 902, 1074, 1261, 1463, 1680, 1912, 2159, 2421, 2698, 2990, 3297, 3619, 3956, 4308, 4675, 5057, 5454, 5866, 6293, 6735, 7192, 7664, 8151, 8653, 9170, 9702, 10249, 10811, 11388, 11980, 12587, 13209, 13846, 14498

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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, A022273, A064761.

Cf. similar sequences listed in A022288.

Programs

Magma

[n*(15*n - 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Mathematica

Table[n (15 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Mar 12 2015 *)
CoefficientList[Series[x (7 + 8 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3,-3,1},{0,7,29},50] (* Harvey P. Dale, Sep 15 2024 *)

PARI

a(n)=n*(15*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 15*n + a(n-1) - 8 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

From Vincenzo Librandi, Mar 31 2015: (Start)

G.f.: x*(7 + 8*x)/(1 - x)^3.

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

From Bruno Berselli, Mar 31 2015: (Start)

a(n) = A022273(-n).

a(n) + a(-n) = A064761(n). (End)

a(n) = A000217(8*n-1) - A000217(7*n-1). - Bruno Berselli, Oct 17 2016

E.g.f.: (x/2)*(15*x + 14)*exp(x). - G. C. Greubel, Aug 23 2017

Extensions

More terms from Vincenzo Librandi, Mar 31 2015