%I #22 Jan 21 2023 18:29:38
%S 1,513,20195,281827,2215269,12030821,50431303,174571335,521638217,
%T 1387420489,3357947691,7517728043,15764279725,31265546157,59104406159,
%U 107162836111,187307353233,316947166865
%N Centered cube numbers: a(n) = (n+1)^9 + n^9.
%C Never prime nor semiprime, as a(n) = (2n+1) * (n^2 + n + 1) * (n^6 + 3n^5 + 12n^4 + 19n^3 + 15n^2 + 6n + 1). - _Jonathan Vos Post_, Aug 26 2011
%C Triprimes (A014612) if n = 2, 5, 6, 14, 21, 75, 90, ... - _R. J. Mathar_, Aug 27 2011
%D B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H Vincenzo Librandi, <a href="/A036087/b036087.txt">Table of n, a(n) for n = 0..10000</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) = A001017(n+1) + A001017(n).
%F G.f.: (1+x)*(x^8 + 502*x^7 + 14608*x^6 + 88234*x^5 + 156190*x^4 + 88234*x^3 + 14608*x^2 + 502*x + 1) / (x-1)^10. - _R. J. Mathar_, Aug 27 2011
%t Total/@Partition[Range[0,20]^9,2,1] (* _Harvey P. Dale_, Jan 31 2015 *)
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,513,20195,281827,2215269,12030821,50431303,174571335,521638217,1387420489},20] (* _Harvey P. Dale_, Jan 21 2023 *)
%o (Magma) [(n+1)^9+n^9: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011
%o (PARI) a(n)=(n+1)^9+n^9 \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A036085, A100267, A154535, A100266, A152913, A194155, A194185, A194216.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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