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A134158 a(n) = 1 + 27n + 252n^2 + 882n^3 + 1029n^4. 7
1, 2191, 24583, 109513, 324013, 759811, 1533331, 2785693, 4682713, 7414903, 11197471, 16270321, 22898053, 31369963, 42000043, 55126981, 71114161, 90349663, 113246263, 140241433, 171797341, 208400851, 250563523, 298821613, 353736073, 415892551, 485901391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A000540(n) is divisible by A000330(n) if and only if n is congruent to {1,2,4,5} mod 7 (see A047380).

This sequence is the case when n is congruent to 1 mod 7.

A134159 is the case when n is congruent to 2 mod 7.

A134160 is the case when n is congruent to 4 mod 7.

A134161 is the case when n is congruent to 5 mod 7.

A133180 is the union of this sequence, A134159, A134160, and A134161.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

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

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

G.f.: -(1 + 2186*x + 13638*x^2 + 8498*x^3 + 373*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) for n>4. - Colin Barker, Aug 12 2017

MATHEMATICA

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

PROG

(PARI) Vec((1 + 2186*x + 13638*x^2 + 8498*x^3 + 373*x^4) / (1 - x)^5 + O(x^30)) \\ Colin Barker, Aug 12 2017

CROSSREFS

Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134155, A134159, A134160, A134161.

Sequence in context: A085442 A208549 A251316 * A227488 A225719 A229319

Adjacent sequences:  A134155 A134156 A134157 * A134159 A134160 A134161

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 10 2007

STATUS

approved

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Last modified September 25 09:07 EDT 2017. Contains 292453 sequences.