A054451 Third column of triangle A054450 (partial row sums of unsigned Chebyshev triangle A049310).

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

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 A352720 A369697

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