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.

Showing 1-4 of 4 results.

A088942 a(n)=60*sum(1<=i<=j<=k<=n,i^2*j/k).

Original entry on oeis.org

0, 60, 390, 1450, 4045, 9421, 19361, 36281, 63326, 104466, 164592, 249612, 366547, 523627, 730387, 997763, 1338188, 1765688, 2295978, 2946558, 3736809, 4688089, 5823829, 7169629, 8753354, 10605230, 12757940, 15246720, 18109455, 21386775
Offset: 0

Views

Author

Benoit Cloitre, Oct 25 2003

Keywords

Comments

Always an integer. Can be expressed as a polynomial with rational coefficients of degree 5.

Links

Crossrefs

Cf. A088941, A088943.

Programs

  • PARI
    a(n)=60*sum(k=1,n,sum(j=1,k,sum(i=1,j,i^2*j/k)))

Formula

a(n) = n/120 * (96n^4 + 765n^3 + 2210n^2 + 2275n + 1354).
G.f.: x*(x^4-5*x^3+10*x^2+30*x+60) / (x-1)^6. - Colin Barker, Jun 15 2013

A088943 a(n)=60*sum(1<=i<=j<=k<=n,i*j^2/k).

Original entry on oeis.org

0, 60, 450, 1790, 5195, 12419, 25999, 49399, 87154, 145014, 230088, 350988, 517973, 743093, 1040333, 1425757, 1917652, 2536672, 3305982, 4251402, 5401551, 6787991, 8445371, 10411571, 12727846, 15438970, 18593380, 22243320, 26444985, 31258665
Offset: 0

Views

Author

Benoit Cloitre, Oct 25 2003

Keywords

Comments

Always an integer. Can be expressed as a polynomial with rational coefficients of degree 5.

Links

Crossrefs

Cf. A088941, A088942.

Programs

  • Mathematica
    LinearRecurrence[{6,-15,20,-15,6,-1},{0,60,450,1790,5195,12419},30] (* Harvey P. Dale, Apr 25 2018 *)
  • PARI
    a(n)=60*sum(k=1,n,sum(j=1,k,sum(i=1,j,i*j^2/k)))

Formula

G.f.: -x*(x^4-5*x^3+10*x^2-90*x-60) / (x-1)^6. - Colin Barker, Jun 15 2013

A088944 a(n) = least k such that for any m>=0 k*sum(1<=u<=v<=w<=m,u^n*v/w) is an integer.

Original entry on oeis.org

6, 12, 60, 60, 84, 84, 60, 60, 132, 132, 5460, 5460, 12, 12, 1020, 1020, 1596, 1596, 660, 660, 276, 276, 5460, 5460, 12, 12, 60, 60, 28644, 28644, 1020, 1020
Offset: 0

Views

Author

Benoit Cloitre, Oct 25 2003

Keywords

Crossrefs

Cf. A088941, A088942, A088943, A088945.

Formula

for n>=1 a(2n+1)=a(2n)

A088945 a(n) =60*sum(1<=u<=v<=w<=m,u^2*v^2/w).

Original entry on oeis.org

0, 60, 690, 3630, 13035, 37059, 89839, 193879, 382834, 704694, 1225368, 2032668, 3240693, 4994613, 7475853, 10907677, 15561172, 21761632, 29895342, 40416762, 53856111, 70827351, 92036571, 118290771, 150507046, 189722170, 237102580
Offset: 0

Views

Author

Benoit Cloitre, Oct 25 2003

Keywords

Comments

Always an integer. Can be expressed as a polynomial with rational coefficients of degree 6.

Links

Crossrefs

Cf. A088941, A088942, A088943, A088944.

Programs

  • Mathematica
    LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,60,690,3630,13035,37059,89839},30] (* Harvey P. Dale, Mar 20 2024 *)

Formula

n*(200*n^5+1752*n^4+5705*n^3+8370*n^2+5075*n+498)/360. - Vladeta Jovovic, Oct 27 2003
G.f.: -x*(x^5-6*x^4+15*x^3+60*x^2+270*x+60) / (x-1)^7. - Colin Barker, Jun 19 2013
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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