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A218745 a(n) = (42^n-1)/41. 1
0, 1, 43, 1807, 75895, 3187591, 133878823, 5622910567, 236162243815, 9918814240231, 416590198089703, 17496788319767527, 734865109430236135, 30864334596069917671, 1296302053034936542183, 54444686227467334771687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of powers of 42 (A009986).

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 (43,-42)

FORMULA

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-42*x)).

a(n) = 43*a(n-1) - 42*a(n-2).

a(n) = floor(42^n/41). (End)

MATHEMATICA

LinearRecurrence[{43, -42}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

PROG

(PARI) A218745(n)=42^n\41

(MAGMA) [n le 2 select n-1 else 43*Self(n-1) - 42*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

(Maxima) A218745(n):=(42^n-1)/41$

makelist(A218745(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: A170676 A170724 A170762 * A262470 A009987 A267532

Adjacent sequences:  A218742 A218743 A218744 * A218746 A218747 A218748

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 04 2012

STATUS

approved

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Last modified November 15 18:10 EST 2018. Contains 317240 sequences. (Running on oeis4.)