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 A222045 Sum of smallest parts of all partitions of n into an even number of parts. 8
 0, 0, 1, 1, 4, 4, 9, 10, 19, 21, 34, 40, 62, 72, 103, 124, 173, 207, 279, 337, 445, 538, 694, 842, 1077, 1299, 1634, 1977, 2464, 2969, 3669, 4411, 5410, 6488, 7896, 9447, 11442, 13640, 16421, 19536, 23411, 27761, 33124, 39174, 46554, 54915, 65008, 76485, 90258 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A222044(n) + a(n) = A046746(n). A222044(n) - a(n) = A222046(n). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz) FORMULA a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*sqrt(3)*n). - Vaclav Kotesovec, Jul 06 2019 EXAMPLE a(6) = 9: partitions of 6 into an even number of parts are [1,1,1,1,1,1], [2,2,1,1], [3,1,1,1], [3,3], [4,2], [5,1], sum of smallest parts is 1+1+1+3+2+1 = 9. MAPLE b:= proc(n, i) option remember; [`if`(n=i, n, 0), 0]+`if`(i<1, [0, 0], b(n, i-1)+ `if`(n [l[2], l[1]])(b(n-i, i)))) end: a:= n-> b(n, n)[2]: seq(a(n), n=0..60); MATHEMATICA b[n_, i_] := b[n, i] = {If[n==i, n, 0], 0} + If[i<1, {0, 0}, b[n, i-1] + If[n

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Last modified August 13 02:28 EDT 2024. Contains 375113 sequences. (Running on oeis4.)