OFFSET
0,1
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).
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
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 *)
PROG
(PARI) a(n)=163+1053*n+2520*n^2+2646*n^3+1029*n^4 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 10 2007
STATUS
approved