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A166753
Partial sums of A166752.
3
1, 2, 5, 6, 17, 18, 61, 62, 233, 234, 917, 918, 3649, 3650, 14573, 14574, 58265, 58266, 233029, 233030, 932081, 932082, 3728285, 3728286, 14913097, 14913098, 59652341, 59652342, 238609313, 238609314, 954437197, 954437198, 3817748729, 3817748730
OFFSET
0,2
FORMULA
G.f.: (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)).
a(n) = a(n+1) + 5*a(n+2) - 5*a(n-3) - 4*a(n-4) + 4*a(n-5).
a(n) = (4/3)*A061547(n+1) - (1/3)*A166754(n).
a(n) = (4/3)*A061547(n+1) - (1/3)*A000975(n) + (4/3)*A011377(n-2).
MATHEMATICA
LinearRecurrence[{1, 5, -5, -4, 4}, {1, 2, 5, 6, 17}, 40] (* G. C. Greubel, May 24 2016 *)
Accumulate[LinearRecurrence[{0, 5, 0, -4}, {1, 1, 3, 1}, 40]] (* Harvey P. Dale, Aug 12 2024 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))) \\ G. C. Greubel, Sep 30 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)) )); // G. C. Greubel, Jun 06 2019
(Sage) ((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019
CROSSREFS
Sequence in context: A227623 A146477 A348439 * A319756 A202854 A274911
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 21 2009
STATUS
approved