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A218567 Number of partitions p of n such that max(p)-min(p) = 4. 4
1, 1, 3, 3, 7, 8, 13, 16, 24, 27, 40, 46, 60, 71, 92, 103, 131, 149, 181, 206, 247, 275, 329, 366, 424, 474, 548, 601, 690, 759, 858, 942, 1059, 1152, 1293, 1404, 1555, 1690, 1869, 2013, 2218, 2390, 2614, 2812, 3066, 3282, 3574, 3820, 4131, 4415, 4769, 5071 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..1000

G. E. Andrews, M. Beck and N. Robbins, Partitions with fixed differences between largest and smallest parts, arXiv:1406.3374 [math.NT], 2014.

FORMULA

G.f.: Sum_{k>0} x^(2*k+4)/Product_{j=0..4} (1-x^(k+j)).

a(n) = A097364(n,4) = A116685(n,4) = A194621(n,4) - A194621(n,3) = A218506(n) - A117143(n).

MATHEMATICA

terms = 52; offset = 6; max = terms + offset; s[k0_ /; k0>0] := Sum[x^(2*k + k0) / Product[ (1 - x^(k+j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x]&; Drop[s[4], offset] (* Jean-Fran├žois Alcover, Sep 11 2017, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A178238 A255333 A200792 * A161416 A241637 A241641

Adjacent sequences:  A218564 A218565 A218566 * A218568 A218569 A218570

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 02 2012

STATUS

approved

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Last modified February 26 12:43 EST 2020. Contains 332280 sequences. (Running on oeis4.)