A009979 Powers of 35.

1, 35, 1225, 42875, 1500625, 52521875, 1838265625, 64339296875, 2251875390625, 78815638671875, 2758547353515625, 96549157373046875, 3379220508056640625, 118272717781982421875, 4139545122369384765625, 144884079282928466796875, 5070942774902496337890625

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 35), L(1, 35), P(1, 35), T(1, 35). Essentially same as Pisot sequences E(35, 1225), L(35, 1225), P(35, 1225), T(35, 1225). See A008776 for definitions of Pisot sequences.

If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4,5,6} such that for fixed y_1,y_2,...,y_n in {1,2,3,4,5,6} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan Janjic, May 24 2007

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 35-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
• Milan Janjic, Enumerative Formulae for Some Functions on Finite Sets.
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (35).

Crossrefs

Cf. A000351, A000420, A008776.

Programs

Magma

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

Mathematica

35^Range[0,15] (* Harvey P. Dale, Sep 10 2011 *)

Formula

G.f.: 1/(1-35*x). - Philippe Deléham, Nov 24 2008

a(n) = 35^n; a(n) = 35*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(35*x).

a(n) = A000351(n)*A000420(n). (End)