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A134160 a(n) = 163 + 1053*n + 2520*n^2 + 2646*n^3 + 1029*n^4. 6
163, 7411, 49981, 180793, 477463, 1042303, 2002321, 3509221, 5739403, 8893963, 13198693, 18904081, 26285311, 35642263, 47299513, 61606333, 78936691, 99689251, 124287373, 153179113, 186837223, 225759151, 270467041, 321507733 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..23.

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*)

CROSSREFS

Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134161.

Sequence in context: A232260 A027543 A222837 * A219127 A049498 A217456

Adjacent sequences:  A134157 A134158 A134159 * A134161 A134162 A134163

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 10 2007

STATUS

approved

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Last modified August 28 00:41 EDT 2015. Contains 261101 sequences.