|
| |
|
|
A145934
|
|
Expansion of 1/(1-x(1-6x)).
|
|
8
| |
|
|
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; 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) [From John M. Campbell, Jul 08 2011].
|
|
|
FORMULA
| a(n)=Sum_{k, 0<=k<=n}A109466(n,k)*6^(n-k).
a(n)=a(n-1)-6*a(n-2); a(0)=1, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2008]
a(n)=(1/46)*I*[(1/2)-(1/2)*I*sqrt(23)]^n*sqrt(23)+(1/2)*[(1/2)-(1/2)*I*sqrt(23)]^n-(1/46)*I *[(1/2)+(1/2)*I*sqrt(23)]^n*sqrt(23)+(1/2)*[(1/2)+(1/2)*I*sqrt(23)]^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 18 2008]
|
|
|
MATHEMATICA
| Join[{a=1, b=1}, Table[c=b-6*a; a=b; b=c, {n, 80}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)
Table[Det[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 + 1]*2 + KroneckerDelta[#1, #2 - 1]*3 &, {n, n}]], {n, 1, 40}] (* From John M. Campbell, Jul 08 2011 *)
|
|
|
PROG
| (Other) sage: [lucas_number1(n, 1, 6) for n in xrange(1, 29)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
|
|
|
CROSSREFS
| Cf. A010892, A107920, A106852, A106853, A106854
Sequence in context: A045452 A152085 A128927 * A033913 A088124 A029456
Adjacent sequences: A145931 A145932 A145933 * A145935 A145936 A145937
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2008
|
| |
|
|
