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A036085 Centered cube numbers: (n+1)^7 + n^7. 9

%I #23 Sep 08 2022 08:44:52

%S 1,129,2315,18571,94509,358061,1103479,2920695,6880121,14782969,

%T 29487171,55318979,98580325,168162021,276272879,439294831,678774129,

%U 1022558705,1506091771,2173871739,3081088541,4295446429,5899183335,7991296871,10689987049,14135325801

%N Centered cube numbers: (n+1)^7 + n^7.

%C Never prime, as a(n) = (2n+1)*(n^6 + 3n^5 + 9n^4 + 13n^3 + 11n^2 + 5n + 1). Semiprimes in the sequence begin for n = 1, 2, 8, 9, 21, 30, 33, 53, 65, 81, 83. - _Jonathan Vos Post_, Aug 26 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="/A036085/b036085.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = A001015(n+1) + A001015(n).

%F G.f.: (1+x)*(x^6 + 120*x^5 + 1191*x^4 + 2416*x^3 + 1191*x^2 + 120*x + 1) / (x-1)^8. - _R. J. Mathar_, Aug 27 2011

%o (Magma) [(n+1)^7+n^7: n in [0..30]]; // _Vincenzo Librandi_, Aug 27 2011

%o (PARI) a(n)=(n+1)^7+n^7 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A100267, A154535, A100266, A152913, A194155, A194185, A194216.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)