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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

%I #19 Dec 31 2023 11:36:11

%S 1,1,13,133,1477,15925,173509,1883413,20471269,222402229,2416608901,

%T 26257155925,285297665317,3099884206069,33681691385797,

%U 365966976355477,3976399872691813,43205412115772725,469446679463465221

%N a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13.

%C 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

%H G. C. Greubel, <a href="/A154999/b154999.txt">Table of n, a(n) for n = 0..950</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,42).

%F a(n+1) = Sum_{k=0..n} A154929(n,k)*6^(n-k).

%F G.f.: (1 - 6*x - 36*x^2)/(1 - 7*x - 42*x^2). - _G. C. Greubel_, Apr 20 2021

%t LinearRecurrence[{7,42}, {1,1,13}, 31] (* _G. C. Greubel_, Apr 20 2021 *)

%t CoefficientList[Series[(1-6x-36x^2)/(1-7x-42x^2),{x,0,20}],x] (* _Harvey P. Dale_, Jan 14 2022 *)

%o (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

%o (Sage)

%o def A154999_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1-6*x-36*x^2)/(1-7*x-42*x^2) ).list()

%o A154999_list(30) # _G. C. Greubel_, Apr 20 2021

%Y Cf. A154929, A154996, A154997, A155000, A155001.

%K nonn

%O 0,3

%A _Philippe Deléham_, Jan 18 2009

%E More terms from _Philippe Deléham_, Jan 27 2009

%E Corrected by _D. S. McNeil_, Aug 20 2010

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)