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A193576 a(n) = T(n)^3 + n^3 where T(n) is a triangular number.

%I A193576 #30 Jun 13 2025 05:14:30
%S A193576 2,35,243,1064,3500,9477,22295,47168,91854,167375,288827,476280,
%T A193576 755768,1160369,1731375,2519552,3586490,5006043,6865859,9269000,
%U A193576 12335652,16204925,21036743,27013824,34343750,43261127,54029835,66945368,82337264,100571625,122053727
%N A193576 a(n) = T(n)^3 + n^3 where T(n) is a triangular number.
%H A193576 Vincenzo Librandi, <a href="/A193576/b193576.txt">Table of n, a(n) for n = 1..10000</a>
%H A193576 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A193576 a(n) = (n^3*(n^3+3*n^2+3*n+9)/8) = (1/8)*(n+3)*(n^2+3)*n^3.
%F A193576 From _Chai Wah Wu_, Jun 12 2025: (Start)
%F A193576 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
%F A193576 G.f.: x*(x^5 - 28*x^3 - 40*x^2 - 21*x - 2)/(x - 1)^7. (End)
%F A193576 a(n) = A000578(n) + A059827(n). - _Alois P. Heinz_, Jun 12 2025
%F A193576 E.g.f.: exp(x)*x*(16 + 124*x + 192*x^2 + 98*x^3 + 18*x^4 + x^5)/8. - _Stefano Spezia_, Jun 13 2025
%o A193576 (Magma) [(n^3*(n^3+3*n^2+3*n+9)/8): n in [1..40]];
%o A193576 (Python)
%o A193576 def A193576(n): return n**3*(n*(n*(n+3)+3)+9)>>3 # _Chai Wah Wu_, Jun 12 2025
%Y A193576 Cf. A000217, A000578, A059827.
%K A193576 nonn,easy
%O A193576 1,1
%A A193576 _Vincenzo Librandi_, Sep 08 2011