A350551 Convolution of Jacobsthal numbers and Pell numbers.

0, 0, 1, 3, 10, 28, 77, 203, 526, 1340, 3377, 8435, 20930, 51660, 126981, 311083, 760070, 1853068, 4509897, 10960243, 26605146, 64520060, 156344317, 378606795, 916354110, 2216907420, 5361353761, 12961984563, 31330062130, 75711587308, 182932193717

Offset

0,4

Comments

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).

References

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

Links

Table of n, a(n) for n=0..30.

Tamás Szakács, Convolution of second order linear recursive sequences I., Annales Mathematicae et Informaticae 46 (2016) pp. 205-216.

Formula

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

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

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

Mathematica

Table[Sum[((2^i - (-1)^i)/3) Fibonacci[n - i, 2], {i, 0, n}], {n, 0,
  30}]

Crossrefs

Cf. A000129, A001045.

Sequence in context: A182737 A320244 A128135 * A191797 A355356 A027252

Adjacent sequences: A350548 A350549 A350550 * A350552 A350553 A350554

Keyword

nonn

Author

Greg Dresden, Jan 04 2022

Status

approved