A218747 a(n) = (44^n-1)/43.

0, 1, 45, 1981, 87165, 3835261, 168751485, 7425065341, 326702875005, 14374926500221, 632496766009725, 27829857704427901, 1224513738994827645, 53878604515772416381, 2370658598693986320765, 104308978342535398113661

Offset

0,3

Comments

Partial sums of powers of 44 (A009988).

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 (45,-44)

Formula

G.f.: x/((1-x)*(1-44*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 45*a(n-1) - 44*a(n-2). - Vincenzo Librandi, Nov 07 2012

a(n) = floor(44^n/43). - Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{45, -44}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
Join[{0}, Accumulate[44^Range[0, 20]]] (* Harvey P. Dale, Dec 28 2015 *)

Prog

(PARI) A218747(n)=44^n\43
(Magma) [n le 2 select n-1 else 45*Self(n-1) - 44*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
(Maxima) A218747(n):=(44^n-1)/43$
makelist(A218747(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: A170678 A170726 A170764 * A121009 A264061 A009989

Adjacent sequences: A218744 A218745 A218746 * A218748 A218749 A218750

Keyword

nonn,easy

Author

M. F. Hasler, Nov 04 2012

Status

approved