%I #24 Jun 02 2023 02:47:34
%S 6,21,45,79,124,181,251,335,434,549,681,831,1000,1189,1399,1631,1886,
%T 2165,2469,2799,3156,3541,3955,4399,4874,5381,5921,6495,7104,7749,
%U 8431,9151,9910,10709,11549,12431,13356,14325,15339,16399,17506,18661,19865
%N a(n) = (n^3 + 24*n^2 + 65*n + 36)/6.
%H Stefano Spezia, <a href="/A087863/b087863.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: (6-3*x-3*x^2+x^3)/(1-x)^4. - _Vincenzo Librandi_, Dec 14 2014
%F E.g.f.: exp(x)*(36 + 90*x + 27*x^2 + x^3)/6. - _Stefano Spezia_, May 30 2023
%e a(0)=A=6; a(1)=a(0)+(A+1)+(A+2)=3A+3, a(2)=a(1)+(A+1)+(A+2)+(A+3)=6A+9, a(3)=a(2)+(A+1)+(A+2)+(A+3)+(A+4)=10A+19, ...
%t Table[(n^3+24n^2+65n+36)/6,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{6,21,45,79},50] (* _Harvey P. Dale_, Dec 15 2014 *)
%t CoefficientList[Series[(6 - 3 x - 3 x^2 + x^3) / (1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 16 2014 *)
%o (PARI) a(n) = (n^3+24*n^2+65*n+36)/6; \\ _Michel Marcus_, Aug 24 2013
%o (Magma) [(n^3+24*n^2+65*n+36)/6: n in [0..40]]; // _Vincenzo Librandi_, Dec 16 2014
%K nonn,easy
%O 0,1
%A Helmut E. Fuchs (helmut2(AT)juno.com), Oct 26 2003
%E New definition from _Vladeta Jovovic_, Oct 27 2003
%E More terms from _Ray Chandler_, Oct 27 2003