A022271 a(n) = n*(13*n + 1)/2.

0, 7, 27, 60, 106, 165, 237, 322, 420, 531, 655, 792, 942, 1105, 1281, 1470, 1672, 1887, 2115, 2356, 2610, 2877, 3157, 3450, 3756, 4075, 4407, 4752, 5110, 5481, 5865, 6262, 6672, 7095, 7531, 7980, 8442, 8917, 9405, 9906, 10420, 10947, 11487, 12040

Offset

0,2

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).

Formula

a(n) = A110449(n, 6) for n>5.

a(n) = 13*n + a(n-1) - 6 with n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

G.f.: x*(7+6*x)/(1-x)^3. - Vincenzo Librandi, Mar 31 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2 - Vincenzo Librandi, Mar 31 2015

a(n) = A022270(-n). - Bruno Berselli, Mar 31 2015

a(n) = A000217(7*n) - A000217(6*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(13*x + 14)*exp(x). - G. C. Greubel, Aug 23 2017

Mathematica

Table[n (13 n + 1)/2, {n, 0, 40}] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3, -3, 1}, {0, 7, 27}, 50] (* Harvey P. Dale, Jul 03 2022 *)

Prog

(Magma) [n*(13*n + 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015
(PARI) a(n)=n*(13*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A022270, A110449.

Cf. similar sequences listed in A022289.

Sequence in context: A344721 A309335 A175367 * A269449 A265900 A159065

Adjacent sequences: A022268 A022269 A022270 * A022272 A022273 A022274

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Mar 31 2015

Status

approved