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 A054451 Third column of triangle A054450 (partial row sums of unsigned Chebyshev triangle A049310). 10
 1, 1, 4, 5, 12, 17, 33, 50, 88, 138, 232, 370, 609, 979, 1596, 2575, 4180, 6755, 10945, 17700, 28656, 46356, 75024, 121380, 196417, 317797, 514228, 832025, 1346268, 2178293, 3524577, 5702870, 9227464, 14930334, 24157816, 39088150, 63245985, 102334135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals triangle A173284 * [1, 2, 3,...]. - Gary W. Adamson, Mar 03 2010 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-3,1,1). FORMULA a(n) = A054450(n+2, 2). G.f.: Fib(x)/(1-x^2)^2, with Fib(x)=1/(1-x-x^2) = g.f. A000045 (Fibonacci numbers without 0). a(2*k) = A027941(k)= F(2*k+3)-1; a(2*k+1)= F(2*(k+2))-(k+2)= A054452(k), k >= 0. a(n-2) = Fibonacci(n+1)-binomial(n-floor(n/2), floor(n/2)), or a(n-2) = sum(i=0, floor(n/2)-1, binomial(n-i, i)) - Jon Perry, Mar 18 2004 a(n) = sum{k=0..floor(n/2), binomial(n-k+2, k)}. - Paul Barry, Oct 23 2004 MAPLE BB:=1/(1-k^2)^2/(1-k-k^2): seq(coeff(series(BB, k, n+1), k, n), n=0..50); # Zerinvary Lajos, May 16 2007 PROG (PARI) Vec(-1/((x-1)^2*(x+1)^2*(x^2+x-1)) + O(x^100)) \\ Colin Barker, Jun 14 2015 CROSSREFS Cf. A054450, A049310, A000045, A052952. Cf. A007382. Cf. A173284. Sequence in context: A342324 A261692 A131328 * A309479 A308775 A305335 Adjacent sequences:  A054448 A054449 A054450 * A054452 A054453 A054454 KEYWORD easy,nonn AUTHOR Wolfdieter Lang, Apr 27 2000 EXTENSIONS More terms from James A. Sellers, Apr 28 2000 STATUS approved

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Last modified August 1 10:13 EDT 2021. Contains 346385 sequences. (Running on oeis4.)