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A322745 a(n) = n * (16*n^2+20*n+5)^2. 3

%I

%S 0,1681,23762,131043,465124,1275125,2948406,6041287,11309768,19740249,

%T 32580250,51369131,77968812,114594493,163845374,228735375,312723856,

%U 419746337,554245218,721200499,926160500,1175272581,1475313862,1833721943,2258625624,2758875625,3344075306

%N a(n) = n * (16*n^2+20*n+5)^2.

%H Colin Barker, <a href="/A322745/b322745.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(n+1) + sqrt(n))^5.

%F sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(n+1) - sqrt(n))^5.

%F From _Colin Barker_, Dec 25 2018: (Start)

%F G.f.: x*(1681 + 13676*x + 13686*x^2 + 1676*x^3 + x^4) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

%F (End)

%e (sqrt(2) + sqrt(1))^5 = 29*sqrt(2) + 41 = sqrt(1682) + sqrt(1681). So a(1) = 1681.

%o (PARI) {a(n) = n*(16*n^2+20*n+5)^2}

%o (PARI) concat(0, Vec(x*(1681 + 13676*x + 13686*x^2 + 1676*x^3 + x^4) / (1 - x)^6 + O(x^30))) \\ _Colin Barker_, Dec 25 2018

%Y Column 5 of A322699.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 25 2018

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Last modified June 1 02:07 EDT 2020. Contains 334758 sequences. (Running on oeis4.)