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 A196039 Total sum of the smallest part of every partition of every shell of n. 2
 0, 1, 4, 9, 18, 30, 50, 75, 113, 162, 231, 318, 441, 593, 798, 1058, 1399, 1824, 2379, 3066, 3948, 5042, 6422, 8124, 10264, 12884, 16138, 20120, 25027, 30994, 38312, 47168, 57955, 70974, 86733, 105676, 128516, 155850, 188644, 227783, 274541 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of A046746. Total sum of parts of all regions of n that contain 1 as a part. - Omar E. Pol, Mar 11 2012 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz) Omar E. Pol, Illustration of the seven regions of 5 FORMULA a(n) = A066186(n) - A196025(n). a(n) ~ exp(Pi*sqrt(2*n/3)) / (2*Pi*sqrt(2*n)). - Vaclav Kotesovec, Jul 06 2019 EXAMPLE For n = 5 the seven partitions of 5 are: 5 3         + 2 4             + 1 2     + 2     + 1 3         + 1 + 1 2     + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 . The five shells of 5 (see A135010 and also A138121), written as a triangle, are: 1 2, 1 3, 1, 1 4, (2, 2), 1, 1, 1 5, (3, 2), 1, 1, 1, 1, 1 . The first "2" of row 4 does not count, also the "3" of row 5 does not count, so we have: 1 2, 1 3, 1, 1 4, 2, 1, 1, 1 5, 2, 1, 1, 1, 1, 1 . thus a(5) = 1+2+1+3+1+1+4+2+1+1+1+5+2+1+1+1+1+1 = 30. MAPLE b:= proc(n, i) option remember;      `if`(n=i, n, 0) +`if`(i<1, 0, b(n, i-1) +`if`(n

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Last modified December 3 14:43 EST 2021. Contains 349463 sequences. (Running on oeis4.)