A327926 -id:A327926 - cp's OEIS frontend

1, 33, 1089, 35937, 1185921, 39135393, 1291467969, 42618442977, 1406408618241, 46411484401953, 1531578985264449, 50542106513726817, 1667889514952984961, 55040353993448503713, 1816331681783800622529, 59938945498865420543457, 1977985201462558877934081, 65273511648264442971824673

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 33), L(1, 33), P(1, 33), T(1, 33). Essentially same as Pisot sequences E(33, 1089), L(33, 1089), P(33, 1089), T(33, 1089). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 33-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

T. D. Noe, Table of n, a(n) for n=0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (33).

Cf. A000244, A001020, A008776, A327926.

[33^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

33^Range[0, 20] (* Paolo Xausa, Jul 12 2025 *)

G.f.: 1/(1-33*x). - Philippe Deléham, Nov 24 2008
a(n) = 33^n; a(n) = 33*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 08 2025: (Start)
E.g.f.: exp(33*x).
a(n) = A000244(n)*A001020(n) = A327926(n)/A000244(n). (End)

cp's OEIS Frontend

A009977 Powers of 33.

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