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%I #10 Sep 08 2022 08:46:04
%S 1,15,113,575,2171,6581,16955,38613,79885,153091,275661,471395,771863,
%T 1217945,1861511,2767241,4014585,5699863,7938505,10867431,14647571,
%U 19466525,25541363,33121565,42492101,53976651
%N Partial sums of A008534, or crystal ball sequence for {A_6}* lattice.
%H Bruno Berselli, <a href="/A222410/b222410.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: (1+8*x+29*x^2+64*x^3+29*x^4+8*x^5+x^6)/(1-x)^7. [_Bruno Berselli_, Feb 28 2013]
%F a(n) = 1+(7/36)*n*(n+1)*(n^4+2*n^3+8*n^2+7*n+18). [_Bruno Berselli_, Feb 28 2013]
%t LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 15, 113, 575, 2171, 6581, 16955}, 26] (* _Bruno Berselli_, Feb 28 2013 *)
%o (Magma) /* By definition: */ A008534:=func<m | IsZero(m) select 1 else (7/6)*m*(m^2+2)*(m^2+3)>; [&+[A008534(i): i in [0..n]]: n in [0..25]]; // _Bruno Berselli_, Feb 28 2013
%Y Cf. A008534.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 23 2013
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