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A218746 a(n) = (43^n-1)/42. 4
0, 1, 44, 1893, 81400, 3500201, 150508644, 6471871693, 278290482800, 11966490760401, 514559102697244, 22126041415981493, 951419780887204200, 40911050578149780601, 1759175174860440565844, 75644532518998944331293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of powers of 43 (A009987).

0 followed by the binomial transform of A170762. - R. J. Mathar, Jul 18 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Index entries related to partial sums

Index entries related to q-numbers

Index entries for linear recurrences with constant coefficients, signature (44,-43)

FORMULA

G.f.: x/((1-x)*(1-43*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 44*a(n-1) - 43*a(n-2). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(43^n/42).  - Vincenzo Librandi, Nov 07 2012

MATHEMATICA

LinearRecurrence[{44, -43}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Join[{0}, Accumulate[43^Range[0, 20]]] (* Harvey P. Dale, Jan 27 2015 *)

PROG

(PARI) A218746(n)=43^n\42

(MAGMA) [n le 2 select n-1 else 44*Self(n-1) - 43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

(Maxima) A218746(n):=(43^n-1)/42$

makelist(A218746(n), n, 0, 30); /* Martin Ettl, 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, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Sequence in context: A170725 A063821 A170763 * A158751 A206992 A206934

Adjacent sequences:  A218743 A218744 A218745 * A218747 A218748 A218749

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 04 2012

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)