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 A218722 a(n) = (19^n-1)/18. 37
 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 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 June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.)