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 A261574 a(n) = n*(n^2 + 3)*(n^6 + 6*n^4 + 9*n^2 + 3). 1

%I

%S 0,76,2786,46764,439204,2744420,12813606,48229636,153992264,432083484,

%T 1092730090,2537720636,5489037036,11179326964,21624372014,40001698260,

%U 71163830416,122319408236,203920464114,330799604044,523606640180,810600392196,1229857906486

%N a(n) = n*(n^2 + 3)*(n^6 + 6*n^4 + 9*n^2 + 3).

%C Also numbers of the form (n-th metallic mean)^9 - 1/(n-th metallic mean)^9, see link to Wikipedia.

%H Colin Barker, <a href="/A261574/b261574.txt">Table of n, a(n) for n = 0..1000</a> (first 100 terms from Raphael Ranna)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = -a(-n) = ( (n+sqrt(n^2+4))/2 )^9-1/( (n+sqrt(n^2+4))/2 )^9.

%F G.f.: 2*x*(38*x^8 +1013*x^7 +11162*x^6 +43907*x^5 +69200*x^4 +43907*x^3 +11162*x^2 +1013*x +38) / (x -1)^10. - _Colin Barker_, Aug 25 2015

%t Table[n (n^2 + 3) (n^6 + 6 n^4 + 9 n^2 + 3), {n, 0, 25}] (* _Bruno Berselli_, Aug 25 2015 *)

%o (PARI) concat(0, Vec(2*x*(38*x^8 +1013*x^7 +11162*x^6 +43907*x^5 +69200*x^4 +43907*x^3 +11162*x^2 +1013*x +38) / (x -1)^10 + O(x^50))) \\ _Colin Barker_, Aug 25 2015

%o (MAGMA) [n*(n^2+3)*(n^6+6*n^4+9*n^2+3): n in [0..25]]; // _Bruno Berselli_, Aug 25 2015

%Y Cf. A001622, A014176, A098316, A098317, A098318, A176398, A176439, A176458, A176522, A261391, A261540.

%K nonn,easy

%O 0,2

%A _Raphael Ranna_, Aug 24 2015

%E Formula in Name by _Colin Barker_, Aug 25 2015

%E Offset changed from 1 to 0 and initial 0 added by _Bruno Berselli_, Aug 25 2015

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Last modified March 29 18:37 EDT 2020. Contains 333117 sequences. (Running on oeis4.)