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A350551 Convolution of Jacobsthal numbers and Pell numbers. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A182737 A320244 A128135 * A191797 A355356 A027252
KEYWORD
nonn
AUTHOR
_Greg Dresden_, Jan 04 2022
STATUS
approved

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)