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 A238864 Number of partitions of n where the difference between consecutive parts is at most 4. 10
 1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 36, 46, 63, 79, 104, 131, 169, 210, 269, 332, 418, 515, 640, 782, 967, 1173, 1435, 1736, 2108, 2534, 3062, 3663, 4398, 5243, 6259, 7429, 8834, 10441, 12356, 14559, 17159, 20144, 23661, 27686, 32403, 37807, 44102, 51306, 59680, 69235, 80297, 92924, 107482, 124070, 143157, 164862, 189763, 218057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of partitions of n such that all parts, with the possible exception of the largest are repeated at most four times (by taking conjugates). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1 + sum(k>=1, q^k/(1-q^k) * prod(i=1..k-1, (1-q^(5*i))/(1-q^i) ) ). a(n) = Sum_{k=0..4} A238353(n,k). - Alois P. Heinz, Mar 09 2014 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(b(n-i*j, i-1), j=0..min(4, n/i))))     end: g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(b(n-i*j, i-1), j=1..n/i)))     end: a:= n-> add(g(n, k), k=0..n): seq(a(n), n=0..60);  # Alois P. Heinz, Mar 09 2014 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i-1], {j, 0, Min[4, n/i]}]]]; g[n_, i_] := g[n, i] = If[n == 0, 1, If[i<1, 0, Sum[b[n - i*j, i - 1], {j, 1, n/i}]]]; a[n_] := Sum[g[n, k], {k, 0, n}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Feb 18 2015, after Alois P. Heinz *) PROG (PARI) N=66;  q = 'q + O('q^N); Vec( 1 + sum(k=1, N, q^k/(1-q^k) * prod(i=1, k-1, (1-q^(5*i))/(1-q^i) ) ) ) CROSSREFS Sequences "number of partitions with max diff d": A000005 (d=0, for n>=1), A034296 (d=1), A224956 (d=2), A238863 (d=3), this sequence, A238865 (d=5), A238866 (d=6), A238867 (d=7), A238868 (d=8), A238869 (d=9), A000041 (d --> infinity). Sequence in context: A026812 A001402 A008629 * A070289 A035961 A051056 Adjacent sequences:  A238861 A238862 A238863 * A238865 A238866 A238867 KEYWORD nonn AUTHOR Joerg Arndt, Mar 08 2014 STATUS approved

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Last modified July 28 15:08 EDT 2021. Contains 346335 sequences. (Running on oeis4.)