OFFSET
0,2
COMMENTS
Binomial transform of [1,2,13,44,205,...] = A002534(n+1).
a(n) is the number of compositions of n when there are 3 types of 1 and 9 types of other natural numbers. - Milan Janjic, Aug 13 2010
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,6).
FORMULA
a(n) = 4*a(n-1) + 6*a(n-2) with a(0)=1, a(1)=3.
a(n) = Sum_{k=0..n} A122016(n,k)*3^k.
a(n) = ((10+sqrt(10))/20)*(2+sqrt(10))^n + ((10-sqrt(10))/20)*(2-sqrt(10))^n. - Richard Choulet, Nov 20 2008
MAPLE
seq(coeff(series((1-x)/(1-4*x-6*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 09 2020
MATHEMATICA
CoefficientList[Series[(1-x)/(1-4x-6x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 6}, {1, 3}, 30] (* Harvey P. Dale, Aug 22 2016 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-x)/(1-4*x-6*x^2)) \\ G. C. Greubel, Jan 09 2020
(Magma) I:=[1, 3]; [n le 2 select I[n] else 4*Self(n-1) + 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 09 2020
(Sage)
def A147518_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x)/(1-4*x-6*x^2) ).list()
A147518_list(30) # G. C. Greubel, Jan 09 2020
(GAP) a:=[1, 3];; for n in [3..30] do a[n]:=4*a[n-1]+6*a[n-2]; od; a; # G. C. Greubel, Jan 09 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Nov 06 2008
STATUS
approved