A188050 - OEIS

%I #23 Sep 08 2022 08:45:56

%S 0,20,100,280,600,1100,1820,2800,4080,5700,7700,10120,13000,16380,

%T 20300,24800,29920,35700,42180,49400,57400,66220,75900,86480,98000,

%U 110500,124020,138600,154280,171100,189100,208320,228800,250580,273700

%N a(n) = A016755(n) - A001845(n).

%C A016755 are odd cubes and A001845 are centered octahedral numbers, so the sequence might be regarded as odd cubes without their octahedral content.

%C A000330 are square pyramidal numbers.

%H Vincenzo Librandi, <a href="/A188050/b188050.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 a(n) = (10/3)*n*(n + 1)*(2*n + 1).

%F a(n) = 20 * A000330(n).

%F G.f.: 20*x*(1+x)/(1-x)^4. - _Klaus Brockhaus_, Mar 20 2011

%p (10/3)*n*(n+1)*(2*n+1)

%t 10n(n+1)(2n+1)/3

%t LinearRecurrence[{4,-6,4,-1},{0,20,100,280},40] (* _Harvey P. Dale_, Jul 18 2016 *)

%o (Magma) A016755:=func< n | (2*n+1)^3 >; A001845:=func< n | (2*n+1)*(2*n^2+2*n+3)/3 >; [ A016755(n)-A001845(n): n in [0..40] ]; // _Klaus Brockhaus_, Mar 20 2011

%Y Cf. A016755, A001845, A000330.

%K nonn,easy

%O 0,2

%A _Damien Pras_, Mar 19 2011