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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A016755, A001845, A000330.

Sequence in context: A128676 A039455 A294112 * A027986 A240437 A174078

Adjacent sequences: A188047 A188048 A188049 * A188051 A188052 A188053

Keyword

nonn,easy

Author

Damien Pras, Mar 19 2011

Status

approved