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A239632 Number of parts in all palindromic compositions of n. 2
0, 1, 3, 4, 10, 12, 28, 32, 72, 80, 176, 192, 416, 448, 960, 1024, 2176, 2304, 4864, 5120, 10752, 11264, 23552, 24576, 51200, 53248, 110592, 114688, 237568, 245760, 507904, 524288, 1081344, 1114112, 2293760, 2359296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (x + 3*x^2 - 2*x^4)/(1 - 2*x^2)^2.

a(n) = Sum_{k=1..n}A051159(n,k)*k.

a(n) = 4*a(n-2) - 4*a(n-4) for n > 3. - Giovanni Resta, Mar 23 2014

EXAMPLE

a(5)=12 because we have: 5, 1+3+1, 2+1+2, 1+1+1+1+1 with a total of 12 parts.

MATHEMATICA

nn=30; r=Solve[p==y/(1-x)-y +1+y ^2x^2/(1-x^2)p, p]; CoefficientList[Series[D[p/.r, y]/.y->1, {x, 0, nn}], x]

CoefficientList[Series[(x + 3 x^2 - 2 x^4)/(1 - 2 x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)

CROSSREFS

Sequence in context: A050187 A101506 A092434 * A031367 A073443 A257494

Adjacent sequences:  A239629 A239630 A239631 * A239633 A239634 A239635

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Mar 22 2014

STATUS

approved

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Last modified October 21 18:54 EDT 2019. Contains 328308 sequences. (Running on oeis4.)