A087752 Powers of 49.

1, 49, 2401, 117649, 5764801, 282475249, 13841287201, 678223072849, 33232930569601, 1628413597910449, 79792266297612001, 3909821048582988049, 191581231380566414401, 9387480337647754305649, 459986536544739960976801, 22539340290692258087863249, 1104427674243920646305299201

Offset: 0

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 02 2003

Keywords

• easy
• nonn

Comments

Same as Pisot sequences E(1, 49), L(1, 49), P(1, 49), T(1, 49). Essentially same as Pisot sequences E(49, 2401), L(49, 2401), P(49, 2401), T(49, 2401). 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 49-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 (49).

Crossrefs

Bisection of A000420.

Cf. A001018 (powers of 8), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009992 (powers of 48).

Cf. A005843, A008776.

Programs

Magma

[49^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

49^Range[0,20] (* or *) Join[{1},NestList[49#&,49,20]] (* Harvey P. Dale, May 10 2019 *)

Maxima

makelist(49^n,n,0,20); /* Martin Ettl, Nov 12 2012 */

PARI

a(n)=49^n \\ M. F. Hasler, Apr 19 2015

Formula

G.f.: 1/(1-49*x). - Philippe Deléham, Nov 24 2008

From Vincenzo Librandi, Nov 21 2010: (Start)

a(n) = 49^n.

a(n) = 49*a(n-1), a(0)=1. (End)

From Elmo R. Oliveira, Jul 08 2025: (Start)

E.g.f.: exp(49*x).

a(n) = A000420(A005843(n)). (End)

Extensions

Edited by M. F. Hasler, Apr 19 2015