A218734 a(n) = (31^n - 1)/30.

0, 1, 32, 993, 30784, 954305, 29583456, 917087137, 28429701248, 881320738689, 27320942899360, 846949229880161, 26255426126284992, 813918209914834753, 25231464507359877344, 782175399728156197665, 24247437391572842127616, 751670559138758105956097

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 31 (A009975).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Shaoshi Chen, Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang, Patterns in Multi-dimensional Permutations, arXiv:2411.02897 [math.CO], 2024. See pp. 2, 17.
• Index entries related to partial sums.
• Index entries for linear recurrences with constant coefficients, signature (32,-31).

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-A218733, A132469, A218736-A218753, A133853, A094028, A218723.

Programs

Magma

[n le 2 select n-1 else 32*Self(n-1)-31*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{32, -31}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)

Maxima

A218734(n):=(31^n-1)/30$
makelist(A218734(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=31^n\30

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1 - x)*(1 - 31*x)).

a(n) = 32*a(n-1) - 31*a(n-2) for n > 1.

a(n) = floor(31^n/30). (End)

E.g.f.: exp(16*x)*sinh(15*x)/15. - Stefano Spezia, Mar 11 2023