|
Search: id:A106852
|
|
|
| A106852 |
|
Expansion of 1/(1-x(1-3x)). |
|
+0
12
|
|
| 1, 1, -2, -5, 1, 16, 13, -35, -74, 31, 253, 160, -599, -1079, 718, 3955, 1801, -10064, -15467, 14725, 61126, 16951, -166427, -217280, 282001, 933841, 87838, -2713685, -2977199, 5163856, 14095453, -1396115, -43682474, -39494129, 91553293, 210035680, -64624199, -694731239, -500858642
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Row sums of Riordan array (1,x(1-3x)) In general, a(n)=sum{k=0..n,(-1)^(n-k)*binomial(k,n-k)*r^(n-k)} yields the row sums of the Riordan array (1,x(1-kx)).
Row sums of Riordan array (1/(1+3x^2),x/(1+3x^2)). - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005
|
|
FORMULA
|
G.f.: 1/(1-x+3x^2); a(n)=2*sqrt(33)*3^(n/2)*cos((n+1)*atan(sqrt(11)/11)-pi*n/2)/11; a(n)=3^(n/2)(cos(-n*acot(sqrt(11)/11))-sqrt(11)*sin(-n*acot(sqrt(11)/11))/11); a(n)=((1+sqrt(-11))^(n+1)-(1-sqrt(-11))^(n+1))/(2^(n+1)sqrt(-11)); a(n)=sum{k=0..n, (-1)^(n-k)*binomial(k, n-k)*3^(n-k)}.
a(n)=sum{k=0..n, C((n+k)/2, k)*(-3)^((n-k)/2)*(1+(-1)^(n-k))/2}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-3)^k}; - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005
a(n)=a(n-1)-3*a(n-2), a(0)=1, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 21 2008]
a(n)=Sum{k, 0<=k<=n}A109466(n,k)*3^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2008]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, 1, +3) for n in xrange(1, 40)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
|
|
CROSSREFS
|
Sequence in context: A104546 A121632 A121579 this_sequence A162975 A120294 A047921
Adjacent sequences: A106849 A106850 A106851 this_sequence A106853 A106854 A106855
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), May 08 2005
|
|
|
Search completed in 0.002 seconds
|
