A139606 - OEIS

%I #34 Apr 16 2024 07:08:33

%S 6,21,36,51,66,81,96,111,126,141,156,171,186,201,216,231,246,261,276,

%T 291,306,321,336,351,366,381,396,411,426,441,456,471,486,501,516,531,

%U 546,561,576,591,606,621,636,651,666,681,696,711,726,741,756,771,786

%N a(n) = 15*n + 6.

%C Numbers of the 6th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

%C 6th transversal numbers (or 6-transversal numbers): (A000217(6)-6)*n + 6.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189. - From _N. J. A. Sloane_, Dec 01 2012

%H Vincenzo Librandi, <a href="/A139606/b139606.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+2,6).

%F G.f.: 3*(2+3*x)/(x-1)^2 . - _R. J. Mathar_, Jul 28 2016

%F From _Elmo R. Oliveira_, Apr 12 2024: (Start)

%F E.g.f.: 3*exp(x)*(2 + 5*x).

%F a(n) = 3*A016873(n) = A008597(n) + 6.

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

%t Range[6, 1000, 15] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%t 15*Range[0,60]+6 (* or *) LinearRecurrence[{2,-1},{6,21},60] (* _Harvey P. Dale_, Aug 09 2019 *)

%o (PARI) a(n)=15*n+6 \\ _Charles R Greathouse IV_, Oct 05 2011

%o (Magma) [15*n+6 : n in [0..60]]; // _Vincenzo Librandi_, Oct 06 2011

%Y Cf. A067076, A144562, A153238.

%Y Cf. A000217, A008597, A016873, A057145, A139600.

%K easy,nonn

%O 0,1

%A _Omar E. Pol_, Apr 27 2008