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A055270 a(n) = 7a(n-1) + (-1^n)*binomial(2,2-n); a(-1)=0. 2
1, 5, 36, 252, 1764, 12348, 86436, 605052, 4235364, 29647548, 207532836, 1452729852, 10169108964, 71183762748, 498286339236, 3488004374652, 24416030622564, 170912214357948, 1196385500505636, 8374698503539452 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7} 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 6*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. 122-125, 194-196.

LINKS

Table of n, a(n) for n=0..19.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (7).

FORMULA

a(n) = (6^2)*(7^(n-2)), n >= 2; a(0)=1, a(1)=5.

G.f.: (1-x)^2/(1-7x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*5^k. - Philippe Deléham, Dec 05 2011

MATHEMATICA

Join[{1, 5}, NestList[7#&, 36, 20]] (* Harvey P. Dale, Sep 04 2017 *)

CROSSREFS

Cf. A052268, A011557. Second differences of A000420.

Sequence in context: A015547 A067376 A098305 * A297576 A164110 A285392

Adjacent sequences:  A055267 A055268 A055269 * A055271 A055272 A055273

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, May 10 2000

STATUS

approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)