OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).
FORMULA
a(3n) = 34*A001109(n).
From Colin Barker, Mar 29 2012: (Start)
a(n) = 6*a(n-3) - a(n-6).
G.f.: 2*x*(3 +10*x +17*x^2 +10*x^3 +3*x^4)/(1 -6*x^3 +x^6). (End)
EXAMPLE
MATHEMATICA
LinearRecurrence[{0, 0, 6, 0, 0, -1}, {6, 20, 34, 56, 126, 204}, 40] (* G. C. Greubel, Aug 18 2021 *)
PROG
(Magma) I:=[6, 20, 34, 56, 126, 204]; [n le 6 select I[n] else 6*Self(n-3) - Self(n-6): n in [1..41]]; // G. C. Greubel, Aug 18 2021
(Sage)
def A106528_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2*x*(3 +10*x +17*x^2 +10*x^3 +3*x^4)/(1 -6*x^3 +x^6) ).list()
a=A106528_list(41); a[1:] # G. C. Greubel, Aug 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Andras Erszegi (erszegi.andras(AT)chello.hu), May 09 2005
STATUS
approved