login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A142965
One fourth of third column (m=2) of triangle A142963.
9
1, 18, 129, 646, 2685, 10002, 34777, 115566, 372453, 1175290, 3654369, 11245110, 34349005, 104373282, 315969705, 954002878, 2874983541, 8652474378, 26015617585, 78169534470, 234766551261, 704840716978, 2115654610809, 6349329417486, 19052920751365, 57169029907482
OFFSET
0,2
LINKS
FORMULA
a(n) = A142963(n+3,2)/4.
From Johannes W. Meijer, Feb 20 2009: (Start)
a(n) = 10a(n-1) - 40a(n-2) + 82a(n-3) - 91a(n-4) + 52a(n-5) - 12a(n-6).
a(n) = 35/2 + 2*n^2 + 12*n - 84*2^n - 24*2^n*n + 135/2*3^n
G.f.: (1 + 8*z - 11*z^2 - 6*z^3)/((1-z)^3*(1-2*z)^2*(1-3*z)).
(End)
MATHEMATICA
LinearRecurrence[{10, -40, 82, -91, 52, -12}, {1, 18, 129, 646, 2685, 10002}, 30] (* or *) CoefficientList[Series[(1+8x-11x^2-6x^3)/((x-1)^3 (2x-1)^2 (3x-1)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 24 2011 *)
PROG
(Magma) [35/2+2*n^2+12*n-84*2^n-24*2^n*n+135/2*3^n: n in [0..25]]; // Vincenzo Librandi, Jun 18 2017
CROSSREFS
Column m=1: 2*A142964; m=3: 8*A142966.
From Johannes W. Meijer, Feb 20 2009: (Start)
Cf. A156925.
Equals A156920(n+2,2).
Equals A156919(n+2,2)/2^n.
(End)
Sequence in context: A041620 A375329 A244879 * A298275 A299137 A299368
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 15 2008
STATUS
approved