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Expansion of g.f. (1 + 7*x)/(1 - 50*x^2).
1

%I #13 Sep 20 2024 13:10:50

%S 1,7,50,350,2500,17500,125000,875000,6250000,43750000,312500000,

%T 2187500000,15625000000,109375000000,781250000000,5468750000000,

%U 39062500000000,273437500000000,1953125000000000,13671875000000000,97656250000000000,683593750000000000,4882812500000000000

%N Expansion of g.f. (1 + 7*x)/(1 - 50*x^2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,50).

%F a(n) = 6*a(n-1) + 7*a(n-2) + 50^floor((n-2)/2).

%F a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*7^(n-2*k).

%F E.g.f.: cosh(5*sqrt(2)*x) + 7*sinh(5*sqrt(2)*x)/(5*sqrt(2)). - _Stefano Spezia_, Mar 31 2023

%t a[n_]:=Sum[Binomial[Floor[n/2],k]7^(n-2k),{k,0,Floor[n/2]}]; Array[a,25,0] (* _Stefano Spezia_, Mar 31 2023 *)

%t LinearRecurrence[{0,50},{1,7},30] (* _Harvey P. Dale_, Sep 20 2024 *)

%Y Cf. A004663, A026383, A016116, A096881.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jul 14 2004

%E More terms from _Stefano Spezia_, Mar 31 2023