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A079284
Diagonal sums of triangle A008949.
2
1, 1, 3, 4, 9, 13, 26, 39, 73, 112, 201, 313, 546, 859, 1469, 2328, 3925, 6253, 10434, 16687, 27633, 44320, 72977, 117297, 192322, 309619, 506037, 815656, 1329885, 2145541, 3491810, 5637351, 9161929, 14799280, 24026745, 38826025, 62983842, 101809867, 165055853, 266865720
OFFSET
0,3
COMMENTS
a(2n) - a(2n-1) = Fibonacci(2n+1).
Diagonal sums of triangle A054450. - Paul Barry, Oct 23 2004
LINKS
Donatella Merlini, Massimo Nocentini, Algebraic Generating Functions for Languages Avoiding Riordan Patterns, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.3.
FORMULA
a(n) = Sum_{j=0..floor(n/2)} Sum_{i=0..j} binomial(n-j, i).
a(n) = Fibonacci(n+3) - 2^floor((n+1)/2). - Vladeta Jovovic, Feb 12 2003
G.f.: (1-x^2)/((1-x-x^2)(1-2x^2)). - Paul Barry, Jan 13 2005
MAPLE
with (combinat):a[0]:=0:a[1]:=1:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] od: seq(a[n], n=1..31); # Zerinvary Lajos, Mar 17 2008
MATHEMATICA
CoefficientList[Series[(1 - x^2) / ((1 - x - x^2) (1 - 2 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{1, 3, -2, -2}, {1, 1, 3, 4}, 40] (* Harvey P. Dale, Nov 30 2018 *)
PROG
(Magma) [Fibonacci(n+3)-2^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 05 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 08 2003
STATUS
approved