The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A275208 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A275208

Expansion of (A(x)^2-A(x^2))/2 where A(x) = A001006(x).
(history; published version)

#16 by Bruno Berselli at Tue May 16 08:51:32 EDT 2017

STATUS

proposed

approved

#15 by Jean-François Alcover at Tue May 16 07:32:02 EDT 2017

STATUS

editing

proposed

#14 by Jean-François Alcover at Tue May 16 07:31:57 EDT 2017

MATHEMATICA

b[n_] := b[n] = If[n<2, 1, ((3*(n-1))*b[n-2] + (1+2*n)*b[n-1])/(n+2)];

a[n_] := a[n] = Sum[b[j]*b[n-j], {j, 0, n/2}] - If[OddQ[n], 0, Function[t, t*(t + 1)/2][b[n/2]]];

Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 16 2017, after Alois P. Heinz *)

STATUS

approved

editing

#13 by Jon E. Schoenfield at Fri Nov 11 19:58:44 EST 2016

STATUS

editing

approved

#12 by Jon E. Schoenfield at Fri Nov 11 19:58:42 EST 2016

COMMENTS

Analogue Analog of A275166 with Motzkin numbers replacing connected graph counts.

STATUS

approved

editing

#11 by Alois P. Heinz at Tue Jul 19 14:38:43 EDT 2016

STATUS

editing

approved

#10 by Alois P. Heinz at Tue Jul 19 14:38:40 EDT 2016

DATA

0, 1, 2, 6, 14, 38, 96, 256, 672, 1805, 4846, 13162, 35874, 98469, 271384, 751656, 2089640, 5831451, 16325950, 45847770, 129106738, 364498596, 1031480792, 2925337352, 8313200232, 23668977163, 67507731786, 192859753310, 551821286374, 1581188102590

STATUS

approved

editing

#9 by Alois P. Heinz at Tue Jul 19 14:37:42 EDT 2016

STATUS

editing

approved

#8 by Alois P. Heinz at Tue Jul 19 14:37:39 EDT 2016

MAPLE

b:= proc(n) option remember; `if`(n<2, 1,

((3*(n-1))*b(n-2)+(1+2*n)*b(n-1))/(n+2))

end:

a:= proc(n) option remember; add(b(j)*b(n-j), j=0..n/2)-

`if`(n::odd, 0, (t-> t*(t+1)/2)(b(n/2)))

end:

seq(a(n), n=0..40); # Alois P. Heinz, Jul 19 2016

#7 by Alois P. Heinz at Tue Jul 19 14:26:38 EDT 2016

LINKS

Alois P. Heinz, <a href="/A275208/b275208.txt">Table of n, a(n) for n = 0..1000</a>

CROSSREFS

Cf. A275207, A026940.

STATUS

approved

editing