A134163 1 + 12*n + 81*n^3 + n*(105*n + 81*n^3)/2.

1, 187, 1531, 5977, 16441, 36811, 71947, 127681, 210817, 329131, 491371, 707257, 987481, 1343707, 1788571, 2335681, 2999617, 3795931, 4741147, 5852761, 7149241, 8650027, 10375531, 12347137, 14587201, 17119051, 19966987, 23156281, 26713177

Offset: 0

Author

Artur Jasinski, Oct 10 2007

Keywords

• nonn
• easy

Comments

A000541(n) is divisible by A000537(n) if and only n is congruent to 1 mod 3 (see A016777).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000537, A000541, A119617, A134153, A134154, A133180, A134158, A134159, A134160.

Programs

Magma

[1 + 12*n + 81*n^3 + n*(105*n+ 81*n^3)/2: n in [0..30]]; // Vincenzo Librandi, May 09 2011

Maple

A134163:=n->1 + 12*n + 81*n^3 + n*(105*n + 81*n^3)/2: seq(A134163(n), n=0..30); # Wesley Ivan Hurt, Oct 23 2014

Mathematica

Table[(3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6, {n, 0, 100}] (* or *) Table[Sum[k^7, {k, 1, 3n + 1}]/Sum[k^3, {k, 1, 3n + 1}], {n, 0, 100}]

Formula

a(n) = (3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6.

a(n) = ( sum_{k=1..3n+1} k^7 ) / ( sum_{k=1..3n+1} k^3 ).

G.f.: (1+182*x+606*x^2+182*x^3+x^4)/(1-x)^5. - R. J. Mathar, Nov 14 2007

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Oct 23 2014