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 A318604 Number of partitions of prime(n) into distinct parts not larger than prime(n-1). 1
 1, 1, 3, 7, 16, 33, 52, 99, 246, 338, 750, 1255, 1608, 2585, 5110, 9782, 12074, 22240, 32987, 40024, 70478, 101693, 173672, 345837, 483325, 570076, 789635, 927404, 1274113, 3725322, 5010683, 7755766, 8953854, 18108385, 20792118, 31316304, 46828022, 61000699 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS The first prime number taken into consideration in the sequence is prime(2)=3, as 2 does not have a preceding prime. LINKS Alois P. Heinz, Table of n, a(n) for n = 2..1000 EXAMPLE a(5) = 7: there are 7 partitions of prime(5) = 11 into distinct parts not larger than prime(4) = 7: [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2], [5,3,2,1]. MAPLE b:= proc(n, i) option remember; (m-> `if`(m (p-> b(p(n), p(n-1)))(ithprime): seq(a(n), n=2..50); # Alois P. Heinz, Aug 29 2018 MATHEMATICA b[n_, i_] := b[n, i] = Function[m, If[m < n, 0, If[m == n, 1, b[n, i - 1] + b[n - i, Min[n - i, i - 1]]]]][i(i+1)/2]; a[n_] := b[Prime[n], Prime[n - 1]]; a /@ Range[2, 50] (* Jean-François Alcover, Nov 30 2020, after Alois P. Heinz *) CROSSREFS Sequence in context: A179904 A298311 A161810 * A084631 A219846 A229914 Adjacent sequences: A318601 A318602 A318603 * A318605 A318606 A318607 KEYWORD nonn AUTHOR Pierandrea Formusa, Aug 29 2018 EXTENSIONS a(26)-a(39) from Alois P. Heinz, Aug 29 2018 STATUS approved

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Last modified September 26 14:24 EDT 2023. Contains 365660 sequences. (Running on oeis4.)