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a(n) = 21*n + 7.
3

%I #31 Apr 16 2024 07:08:28

%S 7,28,49,70,91,112,133,154,175,196,217,238,259,280,301,322,343,364,

%T 385,406,427,448,469,490,511,532,553,574,595,616,637,658,679,700,721,

%U 742,763,784,805,826,847,868,889,910,931,952,973,994

%N a(n) = 21*n + 7.

%C Numbers of the 7th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

%C 7th transversal numbers (or 7-transversal numbers): (A000217(7)-7)*n + 7.

%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="/A139607/b139607.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+2,7).

%F G.f.: 7*(1+2*x)/(x-1)^2. - _R. J. Mathar_, Jul 28 2016

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

%F E.g.f.: 7*exp(x)*(1 + 3*x).

%F a(n) = 7*A016777(n) = A008603(n) + 7 = A152744(n+1) - A152744(n).

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

%t Range[7, 1500, 21] (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2011 *)

%t 21*Range[0,50]+7 (* or *) LinearRecurrence[{2,-1},{7,28},50] (* _Harvey P. Dale_, Feb 23 2020 *)

%o (Magma) [21*n+7: n in [0..60]]; // _Vincenzo Librandi_, Jul 23 2011

%o (PARI) a(n)=21*n+7 \\ _Charles R Greathouse IV_, Oct 05 2011

%Y Cf. A000217, A008603, A016777, A057145, A139600, A152744.

%K easy,nonn

%O 0,1

%A _Omar E. Pol_, Apr 27 2008