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%I #19 Jun 17 2017 03:48:08
%S 1,16,51,106,181,276,391,526,681,856,1051,1266,1501,1756,2031,2326,
%T 2641,2976,3331,3706,4101,4516,4951,5406,5881,6376,6891,7426,7981,
%U 8556,9151,9766,10401,11056,11731,12426,13141,13876,14631,15406,16201,17016,17851
%N 10*n^2 + 5*n + 1.
%C The old definition of this sequence was "Generalized polygonal numbers".
%C Column T(n,5) of A080853.
%C Sequence found by reading the line from 1, in the direction 1, 16,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - _Omar E. Pol_, Sep 10 2011
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = C(5,0) + C(5,1)*n + C(5,2)*n^2.
%F G.f. (C(4,0) + (C(6,2)-2)*x + C(4,2)*x^2)/(1-x)^3 = (1+13*x+6*x^2)/(1-x)^3
%F a(n) = 20*n+a(n-1)-5 with n>0, a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%t Table[10n^2+5n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,16,51},50] (* _Harvey P. Dale_, Aug 05 2014 *)
%o (PARI) a(n)=10*n^2+5*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 0,2
%A _Paul Barry_, Feb 23 2003
%E Definition replaced with the closed form by _Bruno Berselli_, Jan 16 2013
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