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a(n) = 55*n + 11.
3

%I #23 May 05 2024 18:04:53

%S 11,66,121,176,231,286,341,396,451,506,561,616,671,726,781,836,891,

%T 946,1001,1056,1111,1166,1221,1276,1331,1386,1441,1496,1551,1606,1661,

%U 1716,1771,1826,1881,1936,1991,2046,2101,2156,2211,2266

%N a(n) = 55*n + 11.

%C Numbers of the 11th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

%H Vincenzo Librandi, <a href="/A139611/b139611.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = A057145(n+2,11).

%F a(n) = 11 * A016861(n). - _Wesley Ivan Hurt_, Apr 16 2014

%F G.f.: 11*(1+4*x)/(x-1)^2 . - _R. J. Mathar_, Jul 28 2016

%F From _Elmo R. Oliveira_, Apr 16 2024: (Start)

%F E.g.f.: 11*exp(x)*(1 + 5*x).

%F a(n) = 11*(A000566(n+1) - A000566(n)).

%F a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

%p A139611:=n->55*n + 11; seq(A139611(n), n=0..50); # _Wesley Ivan Hurt_, Apr 16 2014

%t Table[55 n + 11, {n, 0, 50}] (* _Wesley Ivan Hurt_, Apr 16 2014 *)

%o (Magma) [11*(5*n + 1): n in [0..60]]; // _Vincenzo Librandi_, Jul 23 2011

%o (PARI) a(n)=55*n+11 \\ _Charles R Greathouse IV_, Oct 05 2011

%Y Cf. A000566, A016861, A057145, A139600.

%K easy,nonn

%O 0,1

%A _Omar E. Pol_, Apr 27 2008