A340493 Sequence whose partial sums give A340492.
1, 3, 8, 23, 49, 125, 241, 540, 1020, 2064, 3710, 7231, 12457, 22883, 39053, 68596, 113751, 194865, 315910, 526019, 840939, 1363524, 2144528, 3419185, 5291079, 8277252, 12668264, 19497436, 29459144, 44762200, 66847518, 100267761, 148318881, 219818270, 322056529, 472600353
Offset: 1
Keywords
Examples
Illustration of initial terms:
A000070: 1 2 4 7 12 19 30
A000041 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1 |_| | | | | | |
2 |_ _| | | | | |
3 |_ _ _ _| | | | |
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5 |_ _ _ _ _ _ _| | | |
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7 |_ _ _ _ _ _ _ _ _ _ _ _| | |
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11 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
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15 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
...
a(n) is the area (or the number of cells) in the n-th region (or section) of the diagram.
For n = 3 the third region of the diagram contains 8 cells, so a(3) = 8.
For n = 7 the seventh region of the diagram contains 241 cells, so a(7) = 241.
Programs
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Mathematica
a[n_] := PartitionsP[n]*Count[Flatten[IntegerPartitions[n]], 1] - PartitionsP[n - 1]*Count[Flatten[IntegerPartitions[n - 1]], 1]; Table[a[n], {n, 1, 36}] (* Robert P. P. McKone, Jan 28 2021 *) -
PARI
f(n) = numbpart(n)*sum(k=0, n-1, numbpart(k)); \\ A340492 a(n) = if (n==1, 1, f(n)-f(n-1)); \\ Michel Marcus, Jan 28 2021
Comments