OFFSET
0,3
COMMENTS
Partial sums of powers of 22; q-integers for q=22: Diagonal k=1 in the triangle A022186.
Partial sums are in A014907. Also, the sequence is related to A014940 by A014940(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. [Bruno Berselli, Nov 06 2012]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..700
Index entries for linear recurrences with constant coefficients, signature (23,-22).
FORMULA
a(n) = floor(22^n/21).
G.f.: x/((1-x)*(1-22*x)). [Bruno Berselli, Nov 06 2012]
a(n) = 23*a(n-1) - 22*a(n-2). - Vincenzo Librandi, Nov 07 2012
E.g.f.: exp(x)*(exp(21*x) - 1)/21. - Elmo R. Oliveira, Aug 29 2024
MATHEMATICA
LinearRecurrence[{23, -22}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) A218725(n)=22^n\21
(Magma) [n le 2 select n-1 else 23*Self(n-1) - 22*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved