The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A287146 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A287146

Number of partitions of n into distinct parts such that the absolute difference between any part and the sum of all smaller parts is not larger than one.
(history; published version)

#17 by Alois P. Heinz at Fri Dec 11 13:40:18 EST 2020

STATUS

proposed

approved

#16 by Jean-François Alcover at Fri Dec 11 09:57:29 EST 2020

STATUS

editing

proposed

#15 by Jean-François Alcover at Fri Dec 11 09:57:25 EST 2020

MATHEMATICA

b[n_, i_] := b[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, 1, b[n, i - 1] + If[i > n || Abs[i - (n - i)] > 1, 0, b[n - i, i - 1]]]];

a[n_] := b[n, n];

a /@ Range[0, 120] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

STATUS

approved

editing

#14 by Alois P. Heinz at Thu Jun 01 20:49:53 EDT 2017

STATUS

editing

approved

#13 by Alois P. Heinz at Thu Jun 01 20:49:49 EDT 2017

FORMULA

a(2^n) = 0 for n > 0.

a(2^n-1) = 1 for n >= 0.

STATUS

approved

editing

#12 by Alois P. Heinz at Sat May 20 20:17:42 EDT 2017

STATUS

editing

approved

#11 by Alois P. Heinz at Sat May 20 20:17:39 EDT 2017

CROSSREFS

Cf. A000009, A002487, A287144.

STATUS

approved

editing

#10 by Alois P. Heinz at Sat May 20 16:24:37 EDT 2017

STATUS

editing

approved

#9 by Alois P. Heinz at Sat May 20 16:21:06 EDT 2017

EXAMPLE

a(25) = 3: (12)6421, (12)7321, (13)6321.

STATUS

approved

editing

#8 by Alois P. Heinz at Sat May 20 16:18:22 EDT 2017

STATUS

editing

approved