|
|
A145934
|
|
Expansion of 1/(1-x*(1-6*x)).
|
|
10
|
|
|
1, 1, -5, -11, 19, 85, -29, -539, -365, 2869, 5059, -12155, -42509, 30421, 285475, 102949, -1609901, -2227595, 7431811, 20797381, -23793485, -148577771, -5816861, 885649765, 920550931, -4393347659, -9916653245, 16443432709
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Row sums of Riordan array (1, x(1-6x)).
For positive n, a(n) equals the determinant of the n X n tridiagonal matrix with 1's along the main diagonal, 3's along the superdiagonal, and 2's along the subdiagonal (see Mathematica code below). - John M. Campbell, Jul 08 2011
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} A109466(n,k)*6^(n-k).
|
|
MATHEMATICA
|
Table[Det[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 + 1]*2 + KroneckerDelta[#1, #2 - 1]*3 &, {n, n}]], {n, 1, 40}] (* John M. Campbell, Jul 08 2011 *)
LinearRecurrence[{1, -6}, {1, 1}, 30] (* G. C. Greubel, Jan 14 2018 *)
|
|
PROG
|
(Sage) [lucas_number1(n, 1, 6) for n in range(1, 29)] # Zerinvary Lajos, Apr 22 2009
(Magma) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 14 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|