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A099508
A transform of the Jacobsthal numbers.
2
0, 1, 1, 3, 3, 8, 9, 21, 25, 54, 68, 139, 183, 358, 489, 924, 1301, 2390, 3450, 6194, 9126, 16080, 24093, 41805, 63507, 108817, 167188, 283533, 439689, 739391, 1155384, 1929504, 3033991, 5038089, 7962758, 13161067, 20889012, 34394215, 54778872
OFFSET
0,4
COMMENTS
A transform of A001045 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3)).
FORMULA
G.f.: x/(1-x-2x^2+2x^3-x^4+x^6); a(n)=a(n-1)+2a(n-2)-2a(n-3)+a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)(-1)^k*J(n-3k)}.
MATHEMATICA
LinearRecurrence[{1, 2, -2, 1, 0, -1}, {0, 1, 1, 3, 3, 8}, 40] (* Harvey P. Dale, Sep 25 2021 *)
CROSSREFS
Cf. A099505.
Sequence in context: A304967 A323654 A092481 * A141577 A245142 A123315
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 20 2004
STATUS
approved