A134161 a(n) = 373 + 1947*n + 3780*n^2 + 3234*n^3 + 1029*n^4.

373, 10363, 61723, 210901, 539041, 1151983, 2180263, 3779113, 6128461, 9432931, 13921843, 19849213, 27493753, 37158871, 49172671, 63887953, 81682213, 102957643, 128141131, 157684261, 192063313, 231779263, 277357783, 329349241

Offset: 0

Author

Artur Jasinski, Oct 10 2007

Keywords

• nonn
• easy

Comments

A000540(n) is divisible by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134160.

Programs

Mathematica

Table[(3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}]
Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}]
LinearRecurrence[{5,-10,10,-5,1},{373,10363,61723,210901,539041},100] (* Harvey P. Dale, Nov 25 2012 *)

PARI

a(n)=373+1947*n+3780*n^2+3234*n^3+1029*n^4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (3*(7*n + 5)^4 + 6*(7*n + 5)^3 - 3*(7*n + 5) + 1)/7.

a(n) = (Sum_{k=1..7*n+5} k^6) / (Sum_{k=1..7*n+5} k^2).

G.f.: -(373+8498*x+13638*x^2+2186*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) with a(0)=373, a(1)=10363, a(2)=61723, a(3)=210901, and a(4)=539041. - Harvey P. Dale, Nov 25 2012