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 A237833 Number of partitions of n such that (greatest part) - (least part) > number of parts. 6
 0, 0, 0, 0, 1, 1, 3, 4, 7, 10, 16, 20, 31, 41, 56, 74, 101, 129, 172, 219, 284, 362, 463, 579, 735, 918, 1147, 1422, 1767, 2172, 2680, 3279, 4013, 4888, 5947, 7200, 8721, 10515, 12663, 15202, 18235, 21798, 26039, 31015, 36898, 43802, 51930, 61426, 72590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS R. J. Mathar, Table of n, a(n) for n = 1..96 George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016. FORMULA A237831(n) + a(n) = A000041(n). - R. J. Mathar, Nov 24 2017 EXAMPLE a(8) = 4 counts these partitions:  7+1, 6+2, 6+1+1, 5+2+1. MAPLE isA237833 := proc(p)     if abs(p[1]-p[-1]) > nops(p) then         return 1;     else         return 0;     end if; end proc: A237833 := proc(n)     local a, p;     a := 0 ;     p := combinat[firstpart](n) ;     while true do         a := a+isA237833(p) ;         if nops(p) = 1 then             break;         end if;         p := nextpart(p) ;     end do:     return a; end proc: seq(A237833(n), n=1..20) ; # R. J. Mathar, Nov 17 2017 MATHEMATICA z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p]; Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}]  (* A237830 *) Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A237831 *) Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A237832 *) Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}]  (* A237833 *) Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A237834 *) CROSSREFS Cf. A237830, A237831, A237832, A237834. Different from, but has the same beginning as, A275633. Sequence in context: A147789 A047625 A147871 * A275633 A004397 A324368 Adjacent sequences:  A237830 A237831 A237832 * A237834 A237835 A237836 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 16 2014 STATUS approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)