A009978 Powers of 34.

1, 34, 1156, 39304, 1336336, 45435424, 1544804416, 52523350144, 1785793904896, 60716992766464, 2064377754059776, 70188843638032384, 2386420683693101056, 81138303245565435904, 2758702310349224820736, 93795878551873643905024, 3189059870763703892770816

Offset

0,2

Comments

Same as Pisot sequences E(1, 34), L(1, 34), P(1, 34), T(1, 34). Essentially same as Pisot sequences E(34, 1156), L(34, 1156), P(34, 1156), T(34, 1156). 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 34-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Links

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 (34).

Formula

G.f.: 1/(1-34*x). - Philippe Deléham, Nov 24 2008

a(n) = 34^n; a(n) = 34*a(n-1), n > 0; a(0)=1. - Vincenzo Librandi, Nov 21 2010

From Elmo R. Oliveira, Jul 10 2025: (Start)

E.g.f.: exp(34*x).

a(n) = A000079(n)*A001026(n). (End)

Mathematica

34^Range[0, 20] (* or *) NestList[34#&, 1, 20] (* Harvey P. Dale, May 03 2025 *)

Prog

(Magma) [34^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

Crossrefs

Cf. A000079, A001026, A008776.

Sequence in context: A091761 A264134 A264019 * A041545 A189434 A167258

Adjacent sequences: A009975 A009976 A009977 * A009979 A009980 A009981

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved