A087752 Powers of 49.

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

Offset

0,2

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).

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)

Mathematica

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

Prog

(Magma) [49^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010
(Maxima) makelist(49^n, n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=49^n \\ M. F. Hasler, Apr 19 2015

Crossrefs

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

Sequence in context: A170768 A218751 A120999 * A069741 A203384 A099367

Adjacent sequences: A087749 A087750 A087751 * A087753 A087754 A087755

Keyword

easy,nonn

Author

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

Extensions

Edited by M. F. Hasler, Apr 19 2015

Status

approved