The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A302348 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A302348

a(n) = Sum_{p in P} (H(2,p)^2)/2, where P is the set of partitions of n, and H(2,p) is the number of hooks of length 2 in p.
(history; published version)

#25 by Peter Luschny at Sun May 20 18:13:48 EDT 2018

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proposed

approved

#24 by Emily Anible at Sat May 19 10:31:22 EDT 2018

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editing

proposed

#23 by Emily Anible at Fri May 18 15:33:29 EDT 2018

FORMULA

G.f: (q^2*(1+q^2+2*q^4))/((1-q^2)*(1-q^4)*Product_{i>0} (1-q^i)). (conjectured)

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approved

editing

#22 by Bruno Berselli at Fri May 18 04:54:12 EDT 2018

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reviewed

approved

#21 by Joerg Arndt at Fri May 18 03:48:41 EDT 2018

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proposed

reviewed

#20 by Jean-François Alcover at Fri May 18 03:07:34 EDT 2018

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editing

proposed

#19 by Jean-François Alcover at Fri May 18 03:07:29 EDT 2018

MATHEMATICA

b[n_, i_, p_, l_] := b[n, i, p, l] = If[n == 0, p^2, If[i > n, 0, b[n, i + 1, p, 1] + Sum[b[n - i*j, i+1, p + If[j > 1, 1, 0]+l, 0], {j, 1, n/i}]]];

a[n_] := b[n, 1, 0, 0]/2;

Table[a[n], {n, 0, 50}] (* Jean-François Alcover, May 18 2018, after Alois P. Heinz *)

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approved

editing

#18 by Alois P. Heinz at Sun Apr 15 12:58:05 EDT 2018

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editing

approved

#17 by Alois P. Heinz at Sun Apr 15 12:58:03 EDT 2018

LINKS

Alois P. Heinz, <a href="/A302348/b302348.txt">Table of n, a(n) for n = 0..1000</a>

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approved

editing

#16 by Alois P. Heinz at Sun Apr 15 12:39:56 EDT 2018

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editing

approved