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A152725 a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2. 10

%I

%S 0,1,63,666,3430,12195,34461,83188,178956,352485,647515,1124046,

%T 1861938,2964871,4564665,6825960,9951256,14186313,19825911,27219970,

%U 36780030,48986091,64393813,83642076,107460900,136679725,172236051,215184438

%N a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2.

%H G. C. Greubel, <a href="/A152725/b152725.txt">Table of n, a(n) for n = 0..5000</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 a(n) = n^6 - (n-1)^6 + (n-2)^6 - ... + ((-1)^n)*0^6.

%F G.f.: x*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1-x)^7. - _R. J. Mathar_, Jul 08 2013

%t k=0;lst={k};Do[k=n^6-k;AppendTo[lst,k],{n,1,5!}];lst

%t LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0,1,63,666,3430,12195,34461}, 50] (* _G. C. Greubel_, Sep 01 2018 *)

%o (PARI) a(n)=n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (MAGMA) [n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2: n in [0..50]]; // _G. C. Greubel_, Sep 01 2018

%Y Cf. A062392, A062393 (for 5th powers), A011934, A152726 (for 7th powers).

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008

%E Offset set to 0 by _R. J. Mathar_, Aug 15 2010

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Last modified October 20 18:19 EDT 2019. Contains 328269 sequences. (Running on oeis4.)