A096882 Expansion of g.f. (1 + 7*x)/(1 - 50*x^2).
1, 7, 50, 350, 2500, 17500, 125000, 875000, 6250000, 43750000, 312500000, 2187500000, 15625000000, 109375000000, 781250000000, 5468750000000, 39062500000000, 273437500000000, 1953125000000000, 13671875000000000, 97656250000000000, 683593750000000000, 4882812500000000000
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,50).
Programs
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Mathematica
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 *) LinearRecurrence[{0,50},{1,7},30] (* Harvey P. Dale, Sep 20 2024 *)
Formula
a(n) = 6*a(n-1) + 7*a(n-2) + 50^floor((n-2)/2).
a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*7^(n-2*k).
E.g.f.: cosh(5*sqrt(2)*x) + 7*sinh(5*sqrt(2)*x)/(5*sqrt(2)). - Stefano Spezia, Mar 31 2023
Extensions
More terms from Stefano Spezia, Mar 31 2023