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A353580 a(n) = 2*a(n-1) + a(n-2) - 1, with a(0) = 0 and a(1) = 2. 1
0, 2, 3, 7, 16, 38, 91, 219, 528, 1274, 3075, 7423, 17920, 43262, 104443, 252147, 608736, 1469618, 3547971, 8565559, 20679088, 49923734, 120526555, 290976843, 702480240, 1695937322, 4094354883, 9884647087, 23863649056, 57611945198, 139087539451, 335787024099, 810661587648 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Andreas M. Hinz and Paul K. Stockmeyer, Precious Metal Sequences and Sierpinski-Type Graphs, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
FORMULA
a(n) = (1/4)((2*s - 1)*(1 + s)^n - (2*s + 1)*(1 - s)^n + 2) where s = sqrt(2).
G.f.: -x*(3*x-2)/((x-1)*(x^2+2*x-1)). - Alois P. Heinz, May 03 2022
E.g.f.: exp(x)*(1 - cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x))/2. - Stefano Spezia, May 03 2022
CROSSREFS
Sequence in context: A153056 A235112 A081207 * A334398 A027118 A114582
KEYWORD
nonn,easy
AUTHOR
Paul K. Stockmeyer, May 03 2022
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)