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A218722 a(n) = (19^n-1)/18. 34
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

Vincenzo Librandi, Table of n, a(n) for n = 0..700

Index entries related to partial sums

Index entries for linear recurrences with constant coefficients, signature (20,-19).

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

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

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Sequence in context: A170653 A170701 A170739 * A158534 A171325 A075843

Adjacent sequences:  A218719 A218720 A218721 * A218723 A218724 A218725

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 04 2012

STATUS

approved

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Last modified February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)