A139608 - OEIS

%I #35 Apr 16 2024 10:26:17

%S 8,36,64,92,120,148,176,204,232,260,288,316,344,372,400,428,456,484,

%T 512,540,568,596,624,652,680,708,736,764,792,820,848,876,904,932,960,

%U 988,1016,1044,1072,1100,1128,1156,1184,1212,1240,1268,1296,1324,1352,1380

%N a(n) = 28*n + 8.

%C Numbers of the 8th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

%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="/A139608/b139608.txt">Table of n, a(n) for n = 0..10000</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+2,8).

%F a(n) = 2*a(n-1) - a(n-2); a(0)=8, a(1)=36. - _Harvey P. Dale_, Dec 14 2012

%F G.f.: 4*(2+5*x)/(x-1)^2. - _R. J. Mathar_, Jul 28 2016

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

%F E.g.f.: 4*exp(x)*(2 + 7*x).

%F a(n) = 4*A017005(n) = A135628(n) + 8 = A316466(n+1) - A316466(n). (End)

%t Range[8, 7000, 28] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%t LinearRecurrence[{2,-1},{8,36},50] (* or *) NestList[28+#&,8,50] (* _Harvey P. Dale_, Dec 14 2012 *)

%o (Magma) [4*(7*n + 2): n in [0..50]]; // _Vincenzo Librandi_, Jul 13 2011

%o (PARI) a(n)=28*n+8 \\ _Charles R Greathouse IV_, Oct 05 2011

%Y Cf. A017005, A057145, A135628, A139600, A316466.

%K easy,nonn

%O 0,1

%A _Omar E. Pol_, Apr 27 2008