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A154999
a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13.
6
1, 1, 13, 133, 1477, 15925, 173509, 1883413, 20471269, 222402229, 2416608901, 26257155925, 285297665317, 3099884206069, 33681691385797, 365966976355477, 3976399872691813, 43205412115772725, 469446679463465221
OFFSET
0,3
COMMENTS
The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - R. J. Mathar, Jan 20 2009
FORMULA
a(n+1) = Sum_{k=0..n} A154929(n,k)*6^(n-k).
G.f.: (1 - 6*x - 36*x^2)/(1 - 7*x - 42*x^2). - G. C. Greubel, Apr 20 2021
MATHEMATICA
LinearRecurrence[{7, 42}, {1, 1, 13}, 31] (* G. C. Greubel, Apr 20 2021 *)
CoefficientList[Series[(1-6x-36x^2)/(1-7x-42x^2), {x, 0, 20}], x] (* Harvey P. Dale, Jan 14 2022 *)
PROG
(Magma) I:=[1, 13]; [1] cat [n le 2 select I[n] else 7*(Self(n-1) +6*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021
(Sage)
def A154999_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-6*x-36*x^2)/(1-7*x-42*x^2) ).list()
A154999_list(30) # G. C. Greubel, Apr 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jan 18 2009
EXTENSIONS
More terms from Philippe Deléham, Jan 27 2009
Corrected by D. S. McNeil, Aug 20 2010
STATUS
approved