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 1-3 of 3 results.

A004441 Numbers that are not the sum of 4 distinct nonzero squares.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 52, 53, 55, 56, 58, 59, 60, 61, 64, 67, 68
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

It has been shown that 157 is the last odd number in this sequence. Beyond 157, the terms grow exponentially. - T. D. Noe, Apr 07 2007
Taking a(86) to a(120) as initial terms, A004441(n) satisfies the 35th-order recurrence relation u(n) = 4*u(n-35). - Ant King, Aug 13 2010

Links

Crossrefs

Cf. A004195, A004196, A004433 (complement).

Programs

  • Mathematica
    data1=Reduce[w^2+x^2+y^2+z^2==# && 00,0,k],{k,1,Length[data2]}],0] (* Ant King, Aug 13 2010 *)

A004196 The numbers not expressible as the sum of 4 distinct nonzero squares can be written D*4^n union E. This is E.

Original entry on oeis.org

21, 29, 35, 41, 45, 49, 53, 59, 61, 69, 77, 83, 89, 101, 115, 157
Offset: 1

Views

Author

N. J. A. Sloane, Dan Hoey

Keywords

Links

Crossrefs

Cf. A004195, A004441.

A175958 Number of partitions of n^2 into 4 distinct nonzero squares.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 5, 0, 4, 4, 5, 0, 10, 4, 7, 0, 11, 7, 17, 1, 13, 17, 15, 0, 29, 13, 27, 4, 23, 17, 41, 0, 29, 35, 32, 4, 66, 24, 38, 0, 47, 35, 73, 7, 50, 56, 73, 1, 91, 42, 63, 17, 68, 49, 125, 0, 103, 93, 83, 13, 133, 86, 93, 4
Offset: 0

Views

Author

R. J. Mathar, Oct 30 2010

Keywords

Examples

			a(9)=1 refers to the partition 9^2 = 2^2+4^2+5^2+6^2. a(11)=1 refers to 11^2 = 1^2+2^2+4^2+10^2. a(13)=2 refers to 13^2 = 1^2+2^2+8^2+10^2 = 2^2+4^2+7^2+10^2.

Links

Crossrefs

Cf. A004195, A004441, A004433, A181524.

Programs

  • Maple
    A025443 := proc(n) local res,a,b,c,d ; res := 0 ; for a from 1 do if 4*a^2 > n then break; fi; for b from a+1 do if a^2+3*b^2 > n then break; fi; for c from b+1 do if a^2+b^2+2*c^2 > n then break; fi; for d from c+1 do if a^2+b^2+c^2+d^2 > n then break; elif a^2+b^2+c^2+d^2 = n then res := res+1 ; fi ; end do; end do; end do: end do: res ; end proc:
A := proc(n) A025443(n^2) ; end proc: seq(A(n),n=0..60) ;
# second Maple program:
b:= proc(n,i,t) option remember; `if`(n=0, `if`(t=0,1,0),
      `if`(t*i^2n, 0, b(n-i^2,i-1,t-1))))
    end:
a:= n-> b(n^2, n, 4):
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 07 2013
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[t*i^2 < n, 0, If[i == 1, 0, b[n, i-1, t]] + If[i^2 > n, 0, b[n-i^2, i-1, t-1]]]]; a[n_] := b[n^2, n, 4]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jun 24 2015, after Alois P. Heinz *)

Formula

a(n) = A025443(n^2).

Extensions

More terms from Alois P. Heinz, Feb 07 2013
Showing 1-3 of 3 results.

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

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