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A080859 6n^2 + 4n + 1. 6


%S 1,11,33,67,113,171,241,323,417,523,641,771,913,1067,1233,1411,1601,

%T 1803,2017,2243,2481,2731,2993,3267,3553,3851,4161,4483,4817,5163,

%U 5521,5891,6273,6667,7073,7491,7921,8363,8817,9283,9761,10251,10753,11267

%N 6n^2 + 4n + 1.

%C The old definition of this sequence was "Generalized polygonal numbers".

%C Column T(n,4) of A080853.

%C Sequence found by reading the line from 1, in the direction 1, 11,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - _Omar E. Pol_, Sep 08 2011

%H <a href="/index/Rec#order_03">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = C(4, 0) + C(4, 1)n + C(4, 2)n^2.

%F G.f. (C(3, 0)+(C(5, 2)-2)*x+C(3, 2)*x^2)/(1-x)^3 = (1+8*x+3*x^2)/(1-x)^3

%F a(n) = A186424(2*n).

%F a(n) = 12*n+a(n-1)-2 with n>0, a(0)=1. - _Vincenzo Librandi_, Aug 08 2010

%F a(n) = (n+1)*A000384(n+1) - n*A000384(n). - _Bruno Berselli_, Dec 10 2012

%Y Cf. A000384, A001318, A033579, A033581, A186424.

%Y Cf. A220083 for a list of numbers of the form n*P(s,n)-(n-1)*P(s,n-1), where P(s,n) is the n-th polygonal number with s sides.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Feb 23 2003

%E Definition replaced with the closed form by _Bruno Berselli_, Dec 10 2012

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Last modified December 18 04:30 EST 2014. Contains 252079 sequences.