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A145066 Partial sums of A002522, starting at n=1.

%I A145066 #27 Oct 30 2024 21:09:47
%S A145066 2,7,17,34,60,97,147,212,294,395,517,662,832,1029,1255,1512,1802,2127,
%T A145066 2489,2890,3332,3817,4347,4924,5550,6227,6957,7742,8584,9485,10447,
%U A145066 11472,12562,13719,14945,16242,17612,19057,20579,22180,23862,25627
%N A145066 Partial sums of A002522, starting at n=1.
%H A145066 G. C. Greubel, <a href="/A145066/b145066.txt">Table of n, a(n) for n = 1..5000</a>
%F A145066 a(1) = 2; a(n) = a(n-1) + n^2 + 1 for n > 1.
%F A145066 From Christoph Pacher (christoph.pacher(AT)ait.ac.at), Jul 23 2010: (Start)
%F A145066 a(n) = Sum_{k=1..n} (k^2 + 1).
%F A145066 a(n) = A000330(n) + n.
%F A145066 a(n) = n*(n+1)*(2*n+1)/6 + n. (End)
%F A145066 G.f.: x*(2-x+x^2)/(1-x)^4. - _Colin Barker_, Apr 04 2012
%F A145066 E.g.f.: (1/6)*x*(12 + 9*x + 2*x^2)*exp(x). - _G. C. Greubel_, Jul 22 2017
%F A145066 a(n) = A081489(n+1) - 1. - _Jianing Song_, Oct 10 2021
%e A145066 a(2) = a(1) + 2^2 + 1 = 2 + 4 + 1 = 7; a(3) = a(2) + 3^2 + 1 = 7 + 9 + 1 = 17.
%t A145066 Accumulate[Range[50]^2+1] (* _Harvey P. Dale_, Dec 07 2016 *)
%o A145066 (PARI) {a=0; for(n=1, 42, print1(a=a+n^2+1, ","))}
%o A145066 (Python)
%o A145066 def A145066(n): return (n*(n*(2*n + 3) + 1))//6 + n # _Chai Wah Wu_, Oct 30 2024
%Y A145066 Cf. A002522 (n^2 + 1), A005563 ((n+1)^2 - 1), A051925 (zero followed by partial sums of A005563), A081489 (partial sums of A002522 starting at n=0).
%K A145066 nonn,easy
%O A145066 1,1
%A A145066 _Vladimir Joseph Stephan Orlovsky_, Sep 30 2008
%E A145066 Edited by _Klaus Brockhaus_, Oct 17 2008