cp's OEIS Frontend

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.

User: M. Lawrence Glasser

M. Lawrence Glasser's wiki page.

M. Lawrence Glasser has authored 3 sequences.

A246759 Nonnegative numbers k such that x^5 - x^4 + k is reducible.

Original entry on oeis.org

0, 2, 9, 48, 324, 1280, 3750, 9072, 19208, 36864, 50625, 65610, 82944, 110000, 175692, 269568, 399854, 576240, 810000, 1114112, 1503378, 1994544, 2606420, 3360000, 4278582, 5387888, 6716184, 8294400
Offset: 1

Author

M. Lawrence Glasser, Sep 02 2014

Keywords

Comments

Next term > 10^7.

Examples

			For k=2, x^5 - x^4 + 2 is reducible: x^5 - x^4 + 2 = (x+1) * (x^4 - 2*x^3 + 2*x^2 - 2*x + 2).
		

Programs

  • Mathematica
    Select[Range[0,83*10^5],!IrreduciblePolynomialQ[x^5-x^4+#]&] (* Harvey P. Dale, Dec 11 2017 *)
  • PARI
    for(n=0, 10^7, if( !polisirreducible(x^5-x^4+n), print1(n,", "))); \\ Joerg Arndt, Sep 06 2014

Extensions

More terms from Joerg Arndt, Sep 06 2014

A179483 A(k,3) where A(k,n) = Sum_{m=1..k} (-1)^(m+1) *binomial(n,m)*m^k.

Original entry on oeis.org

3, -9, 6, 36, 150, 540, 1806, 5796, 18150, 55980, 171006, 519156, 1569750, 4733820, 14250606, 42850116, 128746950, 386634060, 1160688606, 3483638676, 10454061750, 31368476700, 94118013006, 282379204836, 847187946150, 2541664501740, 7625194831806
Offset: 1

Author

M. Lawrence Glasser, Jul 16 2010

Keywords

Crossrefs

Cf. A001117.

Programs

  • Maple
    A179483 := proc(n) add( (-1)^(m+1)*binomial(3,m)*m^n,m=1..n) ; end proc: # R. J. Mathar, Jan 31 2011
  • Mathematica
    Sum[(-1)^(m+1)Binomial[3,m]m^k,{m,1,k}]
  • PARI
    Vec(3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 21 2017

Formula

a(n) = A001117(n), n>=3. - R. J. Mathar, Jul 20 2010
From Colin Barker, May 21 2017: (Start)
G.f.: 3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
a(n) = 3 - 3*2^n + 3^n for n>2.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>5.
(End)

A020496 From the ground state energy of a variant of the Hubbard Hamiltonian for 2 holes on a lattice of n sites.

Original entry on oeis.org

1, 4, 19, 55, 181, 461
Offset: 4

Author

M. Lawrence Glasser and Don Matthis (Utah)

Keywords