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A134161 a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4. 5
373, 10363, 61723, 210901, 539041, 1151983, 2180263, 3779113, 6128461, 9432931, 13921843, 19849213, 27493753, 37158871, 49172671, 63887953, 81682213, 102957643, 128141131, 157684261, 192063313, 231779263, 277357783, 329349241 (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(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 5}]

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

MATHEMATICA

1) Table[(3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}] (*Artur Jasinski*)

LinearRecurrence[{5, -10, 10, -5, 1}, {373, 10363, 61723, 210901, 539041}, 100] (* Harvey P. Dale, Nov 25 2012 *)

PROG

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

CROSSREFS

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

Sequence in context: A213301 A213300 A219444 * A168168 A226850 A208834

Adjacent sequences:  A134158 A134159 A134160 * A134162 A134163 A134164

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 10 2007

STATUS

approved

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Last modified July 25 09:14 EDT 2021. Contains 346286 sequences. (Running on oeis4.)