A028295 a(n) = n^6 - (883/60)*n^5 + (157/3)*n^4 + (2155/12)*n^3 - (4570/3)*n^2 + (42767/15)*n - 967.

133, 1903, 10561, 38015, 106461, 252737, 533397, 1030505, 1858149, 3169675, 5165641, 8102491, 12301949, 18161133, 26163389, 36889845, 51031685, 69403143, 92955217, 122790103, 160176349, 206564729, 263604837, 333162401, 417337317, 518482403, 639222873

Offset

6,1

Comments

Old name was: "Number of stacks of n pikelets, distance 6 flips from a well-ordered stack".

Links

G. C. Greubel, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x^6*(133 + 972*x + 33*x^2 - 604*x^3 + 187*x^4 + 2*x^5 - 3*x^6) / (1-x)^7. - R. J. Mathar, Jun 21 2011

E.g.f.: (1/5!)*(116040 - 69480*x - 30540*x^2 - 2340*x^3 + 95*x^4 + 3*x^5 - (116040 - 185520*x + 96960*x^2 - 25880*x^3 + 3580*x^4 - 34*x^5 - 120*x^6)*exp(x)). - G. C. Greubel, Jan 03 2024

Mathematica

(* Codes from Robert G. Wilson v, Jul 29 2018: Start *)
a[n_]:= n^6 - (883/60)*n^5 + (157/3)*n^4 + (2155/12)*n^3 - (4570/3)*n^2 + (42767/15)*n - 967; Table[a[n], {n, 6, 36}]
CoefficientList[ Series[x^6 (3x^6 -2x^5 -187x^4 +604x^3 -33x^2 -972x - 133)/(x-1)^7, {x, 0, 36}], x]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {133, 1903, 10561, 38015, 106461, 252737, 533397}, 36]
(* End *)

Prog

(Magma) [(60*n^6 -883*n^5 +3140*n^4 +10775*n^3 -91400*n^2 +171068*n -58020)/60: n in [6..46]]; // G. C. Greubel, Jan 03 2024
(SageMath) [(60*n^6 -883*n^5 +3140*n^4 +10775*n^3 -91400*n^2 +171068*n -58020)/60 for n in range(6, 47)] # G. C. Greubel, Jan 03 2024

Crossrefs

Cf. A003777, A003878, A028294.

Sequence in context: A274175 A038491 A020265 * A262121 A254684 A133240

Adjacent sequences: A028292 A028293 A028294 * A028296 A028297 A028298

Keyword

nonn,easy

Author

R. K. Guy

Extensions

Entry revised by N. J. A. Sloane, Jun 15 2014

a(17)-a(32) from Robert G. Wilson v, Jul 29 2018

Status

approved