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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A075681 a(n) = (n-1)*(n-2)^3 - A003878(n-3), with a(1) = a(2) = 0 and a(3) = 2.

Original entry on oeis.org

0, 0, 2, 21, 60, 121, 207, 321, 466, 645, 861, 1117, 1416, 1761, 2155, 2601, 3102, 3661, 4281, 4965, 5716, 6537, 7431, 8401, 9450, 10581, 11797, 13101, 14496, 15985, 17571, 19257, 21046, 22941, 24945, 27061, 29292, 31641, 34111, 36705
Offset: 1

Views

Author

Jon Perry, Oct 12 2002

Keywords

Links

Crossrefs

Cf. A003878.

Programs

  • Magma
    [0,0,2] cat [1/2*n^3+7/2*n^2-23*n+25: n in [4..50]]; // Vincenzo Librandi, Sep 07 2015
  • Maple
    A075681:=n->1/2*n^3+7/2*n^2-23*n+25: (0,0,2,seq(A075681(n), n=4..50)); # Wesley Ivan Hurt, Sep 06 2015
  • Mathematica
    CoefficientList[Series[x^2 (x^4 -x^3 -12 x^2 +13 x +2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 07 2015 *)
LinearRecurrence[{4,-6,4,-1}, {0,0,2,21,60,121,207}, 50] (* G. C. Greubel, Jan 03 2024 *)
  • SageMath
    [(1/2)*(n^3+7*n^2-46*n+50) +(-1)^((n+2)//2)*binomial(5-n,2)*int(n<4) for n in range(1,51)] # G. C. Greubel, Jan 01 2024

Formula

From Ralf Stephan, Mar 13 2003: (Start)
a(n) = (1/2)*(n^3 + 7*n^2 - 46*n + 50), for n>3.
G.f.: x^3*(2 + 13*x - 12*x^2 - x^3 + x^4)/(1-x)^4. (End)
From G. C. Greubel, Jan 01 2024: (Start)
a(n) = (1/2)*(n^3 + 7*n^2 - 46*n + 50) + (-1)^floor((n+2)/2)*binomial(5 -n,2)*[n<4].
E.g.f.: (1/2)*(50 - 38*x + 10*x^2 + x^3)*exp(x) - 25 - 6*x + 3*x^2/2! + x^3/3!. (End)

Extensions

More terms from Ralf Stephan, Mar 13 2003

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.

Original entry on oeis.org

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

Views

Author

R. K. Guy

Keywords

Comments

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

Links

Crossrefs

Cf. A003777, A003878, A028294.

Programs

  • 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
  • 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 *)
  • 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

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

Extensions

Entry revised by N. J. A. Sloane, Jun 15 2014
a(17)-a(32) from Robert G. Wilson v, Jul 29 2018
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