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A079162
a(n) = 5a(n-2) - 2a(n-4).
2
0, 1, 2, 4, 10, 18, 46, 82, 210, 374, 958, 1706, 4370, 7782, 19934, 35498, 90930, 161926, 414782, 738634, 1892050, 3369318, 8630686, 15369322, 39369330, 70107974, 179585278, 319801226, 819187730, 1458790182, 3736768094
OFFSET
0,3
FORMULA
Also a(n) = a(n-1) + 2a(n-2) if n is odd, else a(n) = 2a(n-1) + a(n-2).
a(2n) = 2*A005824(2n), a(2n+1) = A005824(2n) + A005824(2n+1).
G.f.: x*(1+2*x-x^2)/(1-5*x^2+2*x^4).
MATHEMATICA
a[0] = 0; a[1] = 1; a[n_] := a[n] = If[ OddQ[n], a[n - 1] + 2a[n - 2], 2a[n - 1] + a[n - 2]]; Table[a[n], {n, 0, 30}]
LinearRecurrence[{0, 5, 0, -2}, {0, 1, 2, 4}, 40] (* Harvey P. Dale, Jul 05 2022 *)
CROSSREFS
Cf. A005824. a(2n+1) = A052913(n).
Sequence in context: A348396 A104723 A206140 * A257593 A197926 A228705
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Dec 29 2002
EXTENSIONS
Corrected the g.f. and index in formula with A052913 R. J. Mathar, Apr 01 2009, May 02 2009
STATUS
approved