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A054444 Even indexed members of A001629(n), n >= 2, (Fibonacci convolution). 6

%I

%S 1,5,20,71,235,744,2285,6865,20284,59155,170711,488400,1387225,

%T 3916061,10996580,30737759,85573315,237387960,656451269,1810142185,

%U 4978643596,13661617195,37409025455,102238082976,278920277425,759695287349

%N Even indexed members of A001629(n), n >= 2, (Fibonacci convolution).

%H É. Czabarka, R. Flórez, L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Florez/florez12.html">A Discrete Convolution on the Generalized Hosoya Triangle</a>, Journal of Integer Sequences, 18 (2015), #15.1.6.

%H Guo-Niu Han, <a href="http://www-irma.u-strasbg.fr/~guoniu/papers/p77puzzle.pdf">Enumeration of Standard Puzzles</a>

%H Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a> [Cached copy]

%F a(n) = ((2*n+1)*F(2*(n+1))+4*(n+1)*F(2*n+1))/5, with F(n)= A000045(n) (Fibonacci numbers).

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

%F a(n) = sum(k*binom(2n-2k+2, k), k=1..n+1). - _Emeric Deutsch_, Jun 11 2003

%Y Cf. A001870, A001629, A000045. a(n)= A060920(n+1, 1).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_, Apr 07 2000

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Last modified January 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)