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A045849 Number of nonnegative solutions of x1^2 + x2^2 + ... + x7^2 = n. 3
1, 7, 21, 35, 42, 63, 112, 141, 126, 154, 259, 315, 280, 308, 462, 567, 497, 462, 693, 910, 798, 749, 1078, 1281, 1092, 1043, 1407, 1715, 1576, 1449, 1946, 2422, 2016, 1687, 2429, 3045, 2604, 2345, 3066 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for sequences related to sums of squares

FORMULA

Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^7.

G.f.: (1 + theta_3(q))^7/128, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018

PROG

(PARI) seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^7) \\ Andrew Howroyd, Aug 08 2018

(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(7, 100) # Seiichi Manyama, May 28 2017

CROSSREFS

Cf. A010052, A045847.

Sequence in context: A131893 A282248 A282349 * A031008 A147587 A208543

Adjacent sequences:  A045846 A045847 A045848 * A045850 A045851 A045852

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)