A199300 a(n) = (2*n + 1)*7^n.
1, 21, 245, 2401, 21609, 184877, 1529437, 12353145, 98001617, 766718533, 5931980229, 45478515089, 346032180025, 2616003280989, 19668469112621, 147174406808233, 1096686708796833, 8142067989552245, 60251303122686613, 444556912229552577, 3271482918202092041
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-49).
Programs
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Magma
[(2*n+1)*7^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
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Mathematica
a[n_] := (2*n + 1)*7^n; Array[a, 25, 0] (* Amiram Eldar, Dec 10 2022 *) LinearRecurrence[{14,-49},{1,21},30] (* Harvey P. Dale, Mar 26 2025 *)
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PARI
a(n) = (2*n+1)*7^n \\ Amiram Eldar, Dec 10 2022
Formula
a(n) = 14*a(n-1) - 49*a(n-2).
G.f.: (1+7*x)/(1-7*x)^2.
a(n) = 7*a(n-1) + 2*7^n. - Vincenzo Librandi, Nov 05 2011
From Amiram Eldar, Dec 10 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(7)*arccoth(sqrt(7)).
Sum_{n>=0} (-1)^n/a(n) = sqrt(7)*arccot(sqrt(7)). (End)
E.g.f.: exp(7*x)*(1 + 14*x). - Stefano Spezia, May 09 2023
Extensions
a(15) corrected by Vincenzo Librandi, Nov 05 2011