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A137500
Binomial transform of b(n) = (0, 0, A007910).
1
0, 0, 1, 5, 17, 51, 149, 439, 1309, 3927, 11797, 35423, 106301, 318903, 956645, 2869807, 8609293, 25827879, 77483893, 232452191, 697357085, 2092071255, 6276212741, 18828636175, 56485906477, 169457719431, 508373162389, 1525119495359, 4575358494269, 13726075482807
OFFSET
0,4
COMMENTS
b(n) is binomial transform of (0, 0, A077973).
FORMULA
a(n) = 3*a(n-1) + A009545(n-1) for n > 0.
From Andrew Howroyd, Jan 03 2020: (Start)
a(n) = Sum_{k=0..n-2} binomial(n, k+2)*A007910(k).
a(n) = 5*a(n-1) - 8*a(n-2) + 6*a(n-3) for n >= 3.
G.f.: x*2/((1 - 3*x)*(1 - 2*x + 2*x^2)). (End)
MATHEMATICA
LinearRecurrence[{5, -8, 6}, {0, 0, 1}, 40] (* Harvey P. Dale, Sep 27 2020 *)
PROG
(PARI) concat([0, 0], Vec(1/((1 - 3*x)*(1 - 2*x + 2*x^2)) + O(x^40))) \\ Andrew Howroyd, Jan 03 2020
CROSSREFS
Sequence in context: A103685 A116521 A290900 * A146814 A034335 A337033
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Apr 27 2008
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 03 2020
STATUS
approved