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
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).
Programs
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Magma
[n*(13*n + 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015
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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 *) -
PARI
a(n)=n*(13*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017
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
E.g.f.: (x/2)*(13*x + 14)*exp(x). - G. C. Greubel, Aug 23 2017
Extensions
More terms from Vincenzo Librandi, Mar 31 2015