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A187620 a(n) = n^6 - a(n-1), a(0)=1. 1
1, 0, 64, 665, 3431, 12194, 34462, 83187, 178957, 352484, 647516, 1124045, 1861939, 2964870, 4564666, 6825959, 9951257, 14186312, 19825912, 27219969, 36780031, 48986090, 64393814, 83642075, 107460901 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)+a(n-1) is a perfect 6th power, hence a perfect square and a perfect cube.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-14,14,0,-14,14,-6,1).

FORMULA

a(n) = (-1)^n + n*(3-5*n^2+3*n^4+n^5)/2. - R. J. Mathar, Mar 15 2011

a(n) = (-1)^n+A152725(n). - R. J. Mathar, Mar 15 2011

G.f. ( -1-78*x^2-267*x^3-337*x^4-36*x^5-8*x^6+x^7+6*x ) / ( (1+x)*(x-1)^7 ). - R. J. Mathar, Mar 15 2011

MATHEMATICA

CoefficientList[Series[(- 1 - 78 x^2 - 267 x^3 - 337 x^4 - 36 x^5 - 8 x^6 + x^7 + 6 x)/((1 + x) (x - 1)^7), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 04 2013 *)

LinearRecurrence[{6, -14, 14, 0, -14, 14, -6, 1}, {1, 0, 64, 665, 3431, 12194, 34462, 83187}, 30] (* Harvey P. Dale, Apr 30 2020 *)

PROG

(MAGMA) [(-1)^n + n*(3-5*n^2+3*n^4+n^5)/2: n in [0..30]]; // Vincenzo Librandi, Oct 04 2013

CROSSREFS

Cf. A152725.

Sequence in context: A269080 A221509 A283337 * A119287 A318023 A320408

Adjacent sequences:  A187617 A187618 A187619 * A187621 A187622 A187623

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 12 2011

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)