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A038806 Convolution of A008549 with A000302 (powers of 4). 5
0, 1, 10, 69, 406, 2186, 11124, 54445, 259006, 1205790, 5519020, 24918306, 111250140, 492051124, 2159081192, 9409526397, 40766269774, 175707380630, 753876367356, 3221460111958, 13716223138388, 58210889582796 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Hacène Belbachir, Toufik Djellal, Jean-Gabriel Luque, On the self-convolution of generalized Fibonacci numbers, arXiv:1703.00323 [math.CO], 2017.

A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, J. Int. Seq. 10 (2007) # 07.9.7

FORMULA

a(n) = (n+3)*4^n -(n+2)*binomial(2*n+3, n+1)/2.

G.f.: x*(c(x)/(1-4*x))^2, where c(x) = g.f. for Catalan numbers A000108.

a(n+1), n >= 0 is convolution of A000346 with itself; a(n+1), n >= 0 is convolution of Catalan numbers A000108 C(n+1), n >= 0 with A002697; a(-1)=0.

Asymptotics: a(n) ~ 4^n*(n+1-4*sqrt(n/Pi)). - Fung Lam, Mar 28 2014

Recurrence: (n-1)*(n+1)*a(n) = 2*(n+1)*(4*n-3)*a(n-1) - 8*n*(2*n+1)*a(n-2). - Vaclav Kotesovec, Mar 28 2014

MATHEMATICA

CoefficientList[Series[x ((1 - Sqrt[1 - 4 x])/(2 x)/(1 - 4 x))^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 29 2014 *)

PROG

(MAGMA) [(n+3)*4^n -(n+2)*Binomial(2*n+3, n+1)/2: n in [0..25]]; // Vincenzo Librandi, Jun 09 2011

CROSSREFS

Cf. A000108, A000346, A008549, A000302, A002697.

Sequence in context: A026958 A026988 A081280 * A016273 A128737 A320228

Adjacent sequences:  A038803 A038804 A038805 * A038807 A038808 A038809

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified April 24 10:24 EDT 2019. Contains 322422 sequences. (Running on oeis4.)