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A163985 Sum of all isolated parts of all partitions of n. 4
0, 1, 2, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note that for n >= 3 the isolated parts of all partitions of n are n and n-1.

Also, zero together with the numbers A140139.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Omar E. Pol, Illustration of the shell model of partitions (2D view)

Omar E. Pol, Illustration of the shell model of partitions (3D view)

FORMULA

a(n) = n for n<3, a(n) = 2*n-1 for n>=3.

EXAMPLE

For n=4, the five partitions of 4 are {(4);(2,2);(3,1);(2,1,1);(1,1,1,1)}. Since 1 and 2 are repeated parts and 3 and 4 are not repeated parts (or isolated parts) then a(4) = 3 + 4 = 7.

MATHEMATICA

Join[{0, 1, 2}, Table[2 n - 1, {n, 3, 60}]] (* Vincenzo Librandi, Dec 23 2015 *)

PROG

(MAGMA) [0, 1, 2] cat [2*n-1: n in [3..60]]; // Vincenzo Librandi, Dec 23 2015

(PARI) a(n) = if (n<3, n, 2*n-1); \\ Michel Marcus, Dec 23 2015

CROSSREFS

Cf. A000041, A005408, A140139, A163986.

Sequence in context: A247421 A007069 A182463 * A130773 A140139 A184737

Adjacent sequences:  A163982 A163983 A163984 * A163986 A163987 A163988

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Aug 14 2009

STATUS

approved

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Last modified July 27 05:26 EDT 2021. Contains 346305 sequences. (Running on oeis4.)