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A114199 Row sums of a Pascal-Fibonacci triangle. 2
1, 2, 4, 8, 17, 38, 87, 200, 458, 1044, 2373, 5388, 12233, 27782, 63112, 143392, 325805, 740266, 1681935, 3821412, 8682310, 19726316, 44818473, 101828344, 231355953, 525645354, 1194276812, 2713420728, 6164945513, 14006877390 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of double Fibonacci sequence A103609(n+2). Row sums of A114197.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..2806

Sergio Falcón, Binomial Transform of the Generalized k-Fibonacci Numbers, Communications in Mathematics and Applications (2019) Vol. 10, No. 3, 643-651.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2,1)

FORMULA

G.f.: (1-x)^2/(1-4x+5x^2-2x^3-x^4);

a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(n-k, j)*C(k, j)*F(j);

a(n) = Sum_{k=0..n} C(n, k)*F(floor((k+2)/2)).

MATHEMATICA

LinearRecurrence[{4, -5, 2, 1}, {1, 2, 4, 8}, 30] (* Harvey P. Dale, Dec 07 2015 *)

CROSSREFS

Sequence in context: A084635 A294529 A154222 * A006196 A089796 A112482

Adjacent sequences:  A114196 A114197 A114198 * A114200 A114201 A114202

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified June 18 11:25 EDT 2021. Contains 345098 sequences. (Running on oeis4.)