cp's OEIS Frontend

A175113 a(n) = ((2*n + 1)^6 + 1)/2.

%I A175113 #21 Sep 08 2022 08:45:51
%S A175113 1,365,7813,58825,265721,885781,2413405,5695313,12068785,23522941,
%T A175113 42883061,74017945,122070313,193710245,297411661,443751841,645733985,
%U A175113 919132813,1282863205,1759371881,2375052121,3160681525,4151882813
%N A175113 a(n) = ((2*n + 1)^6 + 1)/2.
%C A175113 Convolution of the finite sequence 1, 358, 5279, 11764, 5279, 358, 1 with A000579. Partial sums of A175114.
%C A175113 Subsequence of A001844 because a(n)=(A050492(n+1)-1)^2+A050492(n+1)^2. - _Bruno Berselli_, Dec 28 2010
%C A175113 a(n) is also the first integer in a sum of (2*n + 1)^6 consecutive integers that equals (2*n + 1)^12. - _Patrick J. McNab_, Dec 26 2016
%H A175113 Vincenzo Librandi, <a href="/A175113/b175113.txt">Table of n, a(n) for n = 0..1000</a>
%H A175113 R. J. Mathar, <a href="http://arxiv.org/abs/1002.3844">Point counts of D_k and some A_k and E_k integer lattices inside hypercubes</a>, arXiv:1002.3844, Variable V_6^(g)(n).
%H A175113 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A175113 a(n)= 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7).
%F A175113 G.f.: (1+358*x+5279*x^2+11764*x^3+5279*x^4+358*x^5+x^6)/(1-x)^7.
%F A175113 a(n) = (2*n^2+2*n+1)*(16*n^4+32*n^3+20*n^2+4*n+1). - _Bruno Berselli_, Dec 27 2010
%t A175113 CoefficientList[Series[(1 + 358*x + 5279*x^2 + 11764*x^3 + 5279*x^4 + 358*x^5 + x^6)/(1 - x)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 20 2012 *)
%o A175113 (Magma) I:=[1, 365, 7813, 58825, 265721, 885781, 2413405]; [n le 7 select I[n] else 7*Self(n-1) - 21*Self(n-2) + 35*Self(n-3) - 35*Self(n-4) + 21*Self(n-5) - 7*Self(n-6) + Self(n-7): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2012
%K A175113 easy,nonn
%O A175113 0,2
%A A175113 _R. J. Mathar_, Feb 13 2010