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A055270
a(n) = 7*a(n-1) + (-1)^n * binomial(2,2-n) with a(-1)=0.
3
1, 5, 36, 252, 1764, 12348, 86436, 605052, 4235364, 29647548, 207532836, 1452729852, 10169108964, 71183762748, 498286339236, 3488004374652, 24416030622564, 170912214357948, 1196385500505636, 8374698503539452, 58622889524776164, 410360226673433148, 2872521586714032036
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.
FORMULA
a(n) = 6^2 * 7^(n-2), n >= 2 with a(0)=1, a(1)=5.
G.f.: (1-x)^2/(1-7*x).
a(n) = Sum_{k=0..n} A201780(n,k)*5^k. - Philippe Deléham, Dec 05 2011
E.g.f.: (13 - 7*x + 36*exp(7*x))/49. - G. C. Greubel, Mar 16 2020
MAPLE
A055270:= n-> `if`(n<2, 4*n+1, 36*7^(n-2)); seq(A055270(n), n=0..30); # G. C. Greubel, Mar 16 2020
MATHEMATICA
Join[{1, 5}, NestList[7#&, 36, 20]] (* Harvey P. Dale, Sep 04 2017 *)
PROG
(Magma) [1, 5] cat [36*7^(n-2): n in [2..30]]; // G. C. Greubel, Mar 16 2020
(Sage) [1, 5]+[36*7^(n-2) for n in (2..30)] # G. C. Greubel, Mar 16 2020
CROSSREFS
Cf. A055272 (first differences of 7^n (A000420)).
Sequence in context: A015547 A067376 A098305 * A297576 A164110 A285392
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, May 10 2000
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Mar 16 2020
STATUS
approved