A045995 -id:A045995 - cp's OEIS frontend

A006449 Row sums of Fibonacci-Pascal triangle in A045995.

1, 2, 3, 6, 16, 122, 8003, 18476850, 190844194212235, 192303711247038132600144086, 20672849468072409216994337223266361373129558839387316

Offset: 0

Jeffrey Shallit, Nov 25 1975

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 0..14
J. Shallit, Letter to N. J. A. Sloane, Oct. 1975
R. Whitney, Problem H-254, Fib. Quart., 13 (1975), p. 281.

Cf. A045995.

a006449 = sum . a045995_row  -- Reinhard Zumkeller, May 20 2014

a(n) = sum(k=0, n, fibonacci(binomial(n, k))) \\ Michel Marcus, May 25 2013

A081667 a(n) = Fibonacci(binomial(n+2,2)).

Original entry on oeis.org

1, 2, 8, 55, 610, 10946, 317811, 14930352, 1134903170, 139583862445, 27777890035288, 8944394323791464, 4660046610375530309, 3928413764606871165730, 5358359254990966640871840, 11825896447871834976429068427, 42230279526998466217810220532898

Offset: 0

Paul Barry, Mar 26 2003

Diagonal of Fibonacci-Pascal triangle A045995.

Alois P. Heinz, Table of n, a(n) for n = 0..96
Peter M. Chema, Illustration of first 12 terms on a square spiral
T. Kotek, J. A. Makowsky, Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs, arXiv preprint arXiv:1309.4020 [math.CO], 2013.

Cf. A000045, A000217, A033192, A045995, A054783.

with(combinat): seq(fibonacci((n^2-n)/2),n=2..16); # Zerinvary Lajos, May 18 2008
# second Maple program:
a:= n-> (<<0|1>, <1|1>>^((n+1)*(n+2)/2))[1, 2]:
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 20 2017

Table[Fibonacci[Binomial[n+2,2]],{n,0,20}] (* Harvey P. Dale, Dec 03 2014 *)

[fibonacci(binomial(n,2)) for n in range(2, 17)] # Zerinvary Lajos, Nov 30 2009

a(n) = sqrt(5)2^(-n(n+3)/2)(sqrt(5)+1)^((n^2+3n+2)/2)/10 + sqrt(5)2^(-n(n + 3)/2)(sqrt(5)-1)^((n^2+3n+ 2)/2)(-1)^(n(n+3)/2)/10.
a(n) = A045995(n+2,2).
a(n) = A000045(A000217(n+1)). - Peter M. Chema, Sep 18 2016. See the name.

Name edited by Michel Marcus, Sep 25 2016

A281450 a(n) = Fibonacci(binomial(2*n,n)).

Original entry on oeis.org

1, 1, 8, 6765, 190392490709135, 20672849399056463095319772838289364792345825123228624

Offset: 0

Alois P. Heinz, Jan 21 2017

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..7

Main diagonal of A045995.

Cf. A000045, A000984, A007318, A273397.

a:= n-> (<<0|1>, <1|1>>^binomial(2*n, n))[1, 2]:
seq(a(n), n=0..6);

a(n) = A000045(A007318(2*n,n)) = A000045(A000984(n)).

a(n) = A045995(n,n).

A297965 a(n) = Fibonacci(binomial(n+3, 3)).

Original entry on oeis.org

1, 3, 55, 6765, 9227465, 225851433717, 160500643816367088, 5358359254990966640871840, 13598018856492162040239554477268290, 4244200115309993198876969489421897548446236915, 263621064469290555679241849789653324393054271110084140201023

Offset: 0

Vincenzo Librandi, Jan 10 2018

Fourth diagonal of A045995.

Cf. A000045, A000292, A045995, A081667.

[Fibonacci(Binomial(n+3,3)): n in [0..20]];

Table[Fibonacci[Binomial[n + 3, 3]], {n, 0, 20}]

a(n) = fibonacci(binomial(n+3, 3)) \\ Felix Fröhlich, Jan 12 2018

a(n) = A000045(A000292(n+1)) = A045995(n+3, 3).

cp's OEIS Frontend

A006449 Row sums of Fibonacci-Pascal triangle in A045995.

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A081667 a(n) = Fibonacci(binomial(n+2,2)).

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A281450 a(n) = Fibonacci(binomial(2*n,n)).

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A297965 a(n) = Fibonacci(binomial(n+3, 3)).

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