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A055842 Expansion of (1-x)^2/(1-5*x). 6
1, 3, 16, 80, 400, 2000, 10000, 50000, 250000, 1250000, 6250000, 31250000, 156250000, 781250000, 3906250000, 19531250000, 97656250000, 488281250000, 2441406250000, 12207031250000, 61035156250000, 305175781250000, 1525878906250000, 7629394531250000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences of A005054.

For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007

a(n) is the number of generalized compositions of n when there are 4 *i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

Table of n, a(n) for n=0..23.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (5)

FORMULA

a(n)=16*5^(n-2), a(0)=1, a(1)=3.

EXAMPLE

a(n) = 5a(n-1)+[(-1)^n]*C(2,2-n).

G.f.: (1-x)^2/(1-5x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*3^k. - Philippe Deléham, Dec 05 2011

MATHEMATICA

Join[{1, 3}, 16 5^(Range[2, 30]-2)] (* Harvey P. Dale, Apr 03 2013 *)

PROG

(PARI) Vec((1-x)^2/(1-5*x) + O(x^100)) \\ Altug Alkan, Mar 13 2016

CROSSREFS

Cf. A000351, A005054.

Sequence in context: A005386 A003769 A053572 * A037773 A037661 A290587

Adjacent sequences:  A055839 A055840 A055841 * A055843 A055844 A055845

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 30 2000

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)