A188050 a(n) = A016755(n) - A001845(n).

0, 20, 100, 280, 600, 1100, 1820, 2800, 4080, 5700, 7700, 10120, 13000, 16380, 20300, 24800, 29920, 35700, 42180, 49400, 57400, 66220, 75900, 86480, 98000, 110500, 124020, 138600, 154280, 171100, 189100, 208320, 228800, 250580, 273700

Offset: 0

Author

Damien Pras, Mar 19 2011

Keywords

• nonn
• easy

Comments

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

A000330 are square pyramidal numbers.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A016755, A001845, A000330.

Programs

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

Maple

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

Mathematica

10n(n+1)(2n+1)/3
LinearRecurrence[{4,-6,4,-1},{0,20,100,280},40] (* Harvey P. Dale, Jul 18 2016 *)

Formula

a(n) = (10/3)*n*(n + 1)*(2*n + 1).

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

G.f.: 20*x*(1+x)/(1-x)^4. - Klaus Brockhaus, Mar 20 2011