A187620 a(n) = n^6 - a(n-1), a(0)=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

Offset: 0

Author

Vincenzo Librandi, Mar 12 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A152725.

Programs

Magma

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

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 *)

Formula

From R. J. Mathar, Mar 15 2011: (Start)

a(n) = (-1)^n + n*(3-5*n^2+3*n^4+n^5)/2.

a(n) = (-1)^n + A152725(n).

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 ). (End)