A014931 a(1)=1, a(n) = n*16^(n-1) + a(n-1).
1, 33, 801, 17185, 344865, 6636321, 124076833, 2271560481, 40926266145, 728121033505, 12822748939041, 223928981472033, 3883103678710561, 66933498461897505, 1147797409030816545, 19594541482740368161, 333189190735802745633, 5645851483964153611041, 95370814658487412671265
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (33,-288,256).
Programs
-
Mathematica
RecurrenceTable[{a[1]==1,a[n]==n*16^(n-1)+a[n-1]},a,{n,20}] (* Harvey P. Dale, Sep 17 2019 *) -
PARI
a(n) = (1+16^n*(15*n-1))/225; \\ Jinyuan Wang, Mar 11 2020
-
PARI
Vec(-x/((x-1)*(16*x-1)^2) + O(x^20)) \\ Elmo R. Oliveira, May 21 2025
Formula
G.f.: x/((1 - x)*(1 - 16*x)^2). - Stefano Spezia, Mar 11 2020
From Elmo R. Oliveira, May 21 2025: (Start)
E.g.f.: exp(x)*(1 + exp(15*x)*(240*x - 1))/225.
a(n) = (16^n*(15*n - 1) + 1)/225.
a(n) = 32*a(n-1) - 256*a(n-2) + 1 for n > 2.
a(n) = 33*a(n-1) - 288*a(n-2) + 256*a(n-3) for n > 3. (End)
Extensions
More terms from Elmo R. Oliveira, May 21 2025