A097985 -id:A097985 - cp's OEIS frontend

A097872 Numerator of J(n) = A000356(n)/A000309(n) (average number of 4-colorings of rank 0 in a rooted nonseparable map which is trivalent and has 2n nodes).

1, 5, 35, 147, 99, 4719, 102245, 158015, 71383, 9493939, 117578783, 81161825, 192225375, 10034164575, 176876744175, 874129996575, 506075261175, 43691164214775, 54585584382615, 91204126883805, 75171984897685, 11189060829001575, 315531515377844415, 3726508102129106091

Offset: 1

N. J. A. Sloane, Sep 21 2004

			1, 5/4, 35/24, 147/88, 99/52, 4719/2176, 102245/41344, ...

W. T. Tutte, On the enumeration of four-colored maps, SIAM J. Appl. Math., 17 (1969), 454-460.

Cf. A000356, A000309, A097985.

A295866 Number of decimal digits in the number of partitions of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 0

José Hernández, Feb 13 2018

In his book on analytic number theory, Don Newman tells this amusing story regarding the number of digits in p(n): "This is told of Major MacMahon who kept a list of these partition numbers arranged one under another up into the hundreds. It suddenly occurred to him that, viewed from a distance, the outline of the digits seemed to form a parabola! Thus the number of digits in p(n), the number of partitions of n, is around C*sqrt(n), or p(n) itself is very roughly e^(a*sqrt(n)). The first crude assessment of p(n)!"

D. J. Newman, Analytic number theory, Springer Verlag, 1998, p. 17.

Cf. A000041, A055642, A072212, A097985.

Join[{1}, IntegerLength[PartitionsP[#]] & /@ Range[99]]

a(n) = #digits(numbpart(n)); \\ Michel Marcus, Feb 17 2018

a(n) = A055642(A000041(n)).

cp's OEIS Frontend

A097872 Numerator of J(n) = A000356(n)/A000309(n) (average number of 4-colorings of rank 0 in a rooted nonseparable map which is trivalent and has 2n nodes).

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A295866 Number of decimal digits in the number of partitions of n.

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