A014930 a(1)=1, a(n) = n*15^(n-1) + a(n-1).
1, 31, 706, 14206, 267331, 4823581, 84557956, 1451432956, 24517448581, 408951042331, 6752105339206, 110549175651706, 1797251568229831, 29043982525261081, 466937872906120456, 7473240118999870456, 119136182166119011081, 1892606438208599479831, 29972552158881206901706
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (31,-255,225).
Programs
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PARI
a(n) = (1+15^n*(14*n-1))/196; \\ Jinyuan Wang, Mar 11 2020
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PARI
Vec(-x/((x-1)*(15*x-1)^2) + O(x^20)) \\ Elmo R. Oliveira, May 21 2025
Formula
G.f.: x/((1 - x)*(1 - 15*x)^2). - Stefano Spezia, Mar 11 2020
From Elmo R. Oliveira, May 21 2025: (Start)
E.g.f.: exp(x)*(1 + exp(14*x)*(210*x - 1))/196.
a(n) = (15^n*(14*n - 1) + 1)/196.
a(n) = 30*a(n-1) - 225*a(n-2) + 1 for n > 2.
a(n) = 31*a(n-1) - 255*a(n-2) + 225*a(n-3) for n >= 4. (End)
Extensions
More terms from Elmo R. Oliveira, May 21 2025