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A364636
a(n) = ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n/2.
2
0, 1, 6, 21, 68, 205, 594, 1673, 4616, 12537, 33630, 89309, 235212, 615173, 1599402, 4137105, 10653712, 27327857, 69856182, 178017061, 452390740, 1146776253, 2900399106, 7320463897, 18441561624, 46376946025, 116442406158, 291929022189, 730881930716, 1827523107829
OFFSET
0,3
FORMULA
The sequence can be continued to all ZZ, and a(-n) = -(-1)^n*a(n).
a(n) = [x^n] (x + 2*x^2 - x^3)/(-1 + x*(2 + x))^2.
a(n) = 2*A364553(n) - A093967(n).
MAPLE
A364636 := n -> ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n / 2:
seq(simplify(A364636(n)), n = 0..29);
PROG
(PARI) a(n) = ((1 - quadgen(8))^n + (1 + quadgen(8))^n)*n/2; \\ Michel Marcus, Jul 31 2023
CROSSREFS
Sequence in context: A107653 A123653 A375297 * A318943 A200761 A169687
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Jul 30 2023
STATUS
approved