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a(n) = 5*n^2 + 3*n.
3

%I #25 Aug 21 2022 04:19:44

%S 8,26,54,92,140,198,266,344,432,530,638,756,884,1022,1170,1328,1496,

%T 1674,1862,2060,2268,2486,2714,2952,3200,3458,3726,4004,4292,4590,

%U 4898,5216,5544,5882,6230,6588,6956,7334,7722,8120,8528,8946,9374,9812,10260

%N a(n) = 5*n^2 + 3*n.

%D L. B. W. Jolley, Summation of Series, Dover Publications, 1961, p. 12

%H G. C. Greubel, <a href="/A126264/b126264.txt">Table of n, a(n) for n = 1..5000</a>

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

%F Sum_{i=1..n} a(i) = n*(n+1)*(5n+7)/3 = 2*A162148(n).

%F a(n) = 2*A147875(n+1).

%F From _G. C. Greubel_, Aug 23 2017: (Start)

%F G.f.: 2*x*(x + 4)/(1 - x)^3.

%F E.g.f.: x*(5*x + 8)*exp(x). (End)

%F Sum_{n>=1} 1/a(n) = 5/9 + sqrt(1-2/sqrt(5))*Pi/6 + log(phi)*sqrt(5)/6 - 5*log(5)/12, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 21 2022

%e a(24) = 5*24^2 + 3*24 = 2880 + 72 = 2952.

%p a:=n->5*n^2+3*n: seq(a(n),n=1..55); # _Emeric Deutsch_, Apr 17 2007

%t Table[n*(5*n + 3), {n,1,50}] (* _G. C. Greubel_, Aug 23 2017 *)

%o (PARI) a(n)=5*n^2+3*n \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A001622, A147875.

%K nonn,easy

%O 1,1

%A _Gary W. Adamson_, Dec 22 2006

%E More terms from _Emeric Deutsch_, Apr 17 2007