A079124 Number of ways to partition n into distinct positive integers <= phi(n), where phi is Euler's totient function (A000010).

1, 1, 0, 1, 0, 2, 0, 4, 1, 5, 1, 11, 0, 17, 4, 13, 13, 37, 2, 53, 13, 51, 35, 103, 10, 135, 78, 167, 89, 255, 4, 339, 253, 378, 306, 542, 121, 759, 558, 872, 498, 1259, 121, 1609, 1180, 1677, 1665, 2589, 808, 3250, 1969, 3844, 3325, 5119, 1850, 6268, 4758, 7546, 7070

Offset

0,6

References

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education, Vol. 31, No. 1, pp. 24-28, Winter 1997. MathEduc Database (Zentralblatt MATH, 1997c.01891).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 2004, pp. 12-17. Zentralblatt MATH, Zbl 1071.05501.

Formula

a(n) = b(0, n), b(m, n) = 1 + sum(b(i, j): m<i<j<phi(n) & i+j=n).

Maple

with(numtheory):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i-1))))
    end:
a:= n-> b(n, phi(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, May 11 2015

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i-1]]]]; a[n_] := b[n, EulerPhi[n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 30 2015, after Alois P. Heinz *)

Prog

(Haskell)
a079124 n = p [1 .. a000010 n] n where
   p _      0 = 1
   p []     _ = 0
   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
-- Reinhard Zumkeller, Jul 05 2013

Crossrefs

Cf. A079126, A000009, A079122, A079125, A067953.

Cf. A227296, A036998.

Sequence in context: A020781 A327883 A007432 * A242071 A176910 A243981

Adjacent sequences: A079121 A079122 A079123 * A079125 A079126 A079127

Keyword

nonn

Author

Reinhard Zumkeller, Dec 27 2002

Extensions

a(0)=1 prepended by Alois P. Heinz, May 11 2015

Status

approved