login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045853 Number of nonnegative solutions of x1^2 + x2^2 + ... + x12^2 = n. 1
1, 12, 66, 220, 507, 924, 1584, 2772, 4521, 6436, 8712, 12552, 18041, 23364, 28776, 37896, 50997, 62832, 72996, 89892, 115776, 139348, 156816, 185064, 231759, 274044, 300828, 343564, 418638, 487080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^12.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2000 from T. D. Noe)

PROG

(Ruby)

def mul(f_ary, b_ary, m)

  s1, s2 = f_ary.size, b_ary.size

  ary = Array.new(s1 + s2 - 1, 0)

  (0..s1 - 1).each{|i|

    (0..s2 - 1).each{|j|

      ary[i + j] += f_ary[i] * b_ary[j]

    }

  }

  ary[0..m]

end

def power(ary, n, m)

  if n == 0

    a = Array.new(m + 1, 0)

    a[0] = 1

    return a

  end

  k = power(ary, n >> 1, m)

  k = mul(k, k, m)

  return k if n & 1 == 0

  return mul(k, ary, m)

end

def A(k, n)

  ary = Array.new(n + 1, 0)

  (0..Math.sqrt(n).to_i).each{|i| ary[i * i] = 1}

  power(ary, k, n)

end

p A(12, 100) # Seiichi Manyama, May 28 2017

CROSSREFS

Cf. A010052, A045847.

Sequence in context: A080559 A284641 A226235 * A277104 A014787 A007249

Adjacent sequences:  A045850 A045851 A045852 * A045854 A045855 A045856

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)