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A114203 Row sums of a Pascal-Jacobsthal triangle. 2
1, 2, 4, 8, 18, 44, 110, 272, 662, 1596, 3838, 9240, 22286, 53812, 129974, 313888, 757878, 1829644, 4416910, 10662952, 25742302, 62147556, 150038438, 362226480, 874493446, 2111213372, 5096916094, 12305037368, 29706982638, 71719002644 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of double Jacobsthal sequence 1,1,1,1,3,3,5,5,11,11,... Row sums of A114202.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..2613

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,-5,2,2).

FORMULA

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

a(n) = 4a(n-1) - 5a(n-2) + 2a(n-3) + 2a(n-4);

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

a(n) = Sum_{k=0..n} C(n, k)*J(floor((k+2)/2)), J(n)=A001045(n).

MATHEMATICA

LinearRecurrence[{4, -5, 2, 2}, {1, 2, 4, 8}, 40] (* Harvey P. Dale, Jun 05 2012 *)

CROSSREFS

Sequence in context: A193617 A233139 A308246 * A100132 A176720 A088457

Adjacent sequences:  A114200 A114201 A114202 * A114204 A114205 A114206

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)