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A218722 a(n) = (19^n-1)/18. 40
0, 1, 20, 381, 7240, 137561, 2613660, 49659541, 943531280, 17927094321, 340614792100, 6471681049901, 122961939948120, 2336276859014281, 44389260321271340, 843395946104155461, 16024522975978953760, 304465936543600121441 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Partial sums of powers of 19 (A001029); q-integers for q=19: diagonal k=1 in triangle A022183.
Partial sums are in A014903. Also, the sequence is related to A014936 by A014936(n) = n*a(n)-sum(a(i), i=0..n-1) for n>0. - Bruno Berselli, Nov 06 2012
LINKS
FORMULA
a(n) = floor(19^n/18).
G.f.: x/((1-x)*(1-19*x)). - Bruno Berselli, Nov 06 2012
a(n) = 20*a(n-1) - 19*a(n-2). - Vincenzo Librandi, Nov 07 2012
E.g.f.: exp(10*x)*sinh(9*x)/9. - Stefano Spezia, Mar 11 2023
MATHEMATICA
LinearRecurrence[{20, -19}, {0, 1}, 40] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) A218722(n)=19^n\18
(Maxima) A218722(n):=(19^n-1)/18$ makelist(A218722(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Magma) [n le 2 select n-1 else 20*Self(n-1)-19*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
CROSSREFS
Sequence in context: A170653 A170701 A170739 * A358109 A358853 A158534
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371276 sequences. (Running on oeis4.)