%I #15 Jan 05 2022 10:31:27

%S 0,0,1,3,10,28,77,203,526,1340,3377,8435,20930,51660,126981,311083,

%T 760070,1853068,4509897,10960243,26605146,64520060,156344317,

%U 378606795,916354110,2216907420,5361353761,12961984563,31330062130,75711587308,182932193717

%N Convolution of Jacobsthal numbers and Pell numbers.

%C a(n) is the convolution of the Jacobsthal numbers A001045 with the Pell numbers A000129. To be precise, a(n) = Sum_{i=0..n} A001045(i)*A000129(n-i).

%D G. Dresden and M. Tulskikh, Convolutions of Sequences with Single-Term Signature Differences, preprint.

%H Tamás Szakács, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_46_from205to216.pdf ">Convolution of second order linear recursive sequences I.</a>, Annales Mathematicae et Informaticae 46 (2016) pp. 205-216.

%F a(n) = Sum_{i=0..n} J(i)*P(n-i) for P(n) = A000129(n), J(n) = A001045(n).

%F a(n) = (P(n+1) + P(n) - J(n+2))/2 for P(n) = A000129(n), J(n) = A001045(n).

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

%t Table[Sum[((2^i - (-1)^i)/3) Fibonacci[n - i, 2], {i, 0, n}], {n, 0,

%t 30}]

%Y Cf. A000129, A001045.

%K nonn

%O 0,4

%A _Greg Dresden_, Jan 04 2022