A134160 a(n) = 163 + 1053*n + 2520*n^2 + 2646*n^3 + 1029*n^4.

163, 7411, 49981, 180793, 477463, 1042303, 2002321, 3509221, 5739403, 8893963, 13198693, 18904081, 26285311, 35642263, 47299513, 61606333, 78936691, 99689251, 124287373, 153179113, 186837223, 225759151, 270467041, 321507733

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, A134161.

Programs

Mathematica

Table[(3(7n + 4)^4 + 6(7n + 4)^3 - 3 (7n + 4) + 1)/7, {n, 0, 100}] (*Artur Jasinski*)
Table[Sum[k^6, {k, 1, 7n + 4}]/Sum[k^2, {k, 1, 7n + 4}], {n, 0, 100}] (*Artur Jasinski*)
LinearRecurrence[{5,-10,10,-5,1},{163,7411,49981,180793,477463},30] (* Harvey P. Dale, Jul 20 2024 *)

PARI

a(n)=163+1053*n+2520*n^2+2646*n^3+1029*n^4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

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

a(n) = sum(k=1..7*n+4, k^6) / sum(k=1..7*n+4, k^2).

G.f.: (163+6596*x+14556*x^2+3368*x^3+13*x^4)/(1-x)^5. - Colin Barker, May 25 2012