A079675 a(1)=1; a(n)=sum(u=1,n-1,sum(v=1,u,sum(w=1,v,sum(x=1, w,sum(y=1,x,a(y)))))).

1, 1, 6, 26, 106, 431, 1757, 7168, 29244, 119305, 486716, 1985603, 8100456, 33046585, 134816705, 549997641, 2243767969, 9153665985, 37343255690, 152345382480, 621507555626, 2535499503900, 10343812679475, 42198572937400

Offset: 1

Author

Benoit Cloitre, Jan 26 2003

Keywords

• nonn
• easy

Comments

Row sums of Riordan array (1,1/(1-x)^5). A quintisection of A003520. - Paul Barry, Feb 02 2006

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1639
• D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
• Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
• Index entries for linear recurrences with constant coefficients, signature (6,-10,10,-5,1).

Crossrefs

Cf. A055991, A052529, A001906.

Programs

Mathematica

LinearRecurrence[{6,-10,10,-5,1},{1,1,6,26,106,431},40] (* Harvey P. Dale, Aug 21 2017 *)

Formula

a(1)=1, a(2)=1, a(3)=6, a(4)=26, a(5)=106, a(6)=431; for n>=7, a(n)=5*u(n-1)-4*u(n-2)+u(n-3)+b(n) where b(n) is the 6 periodic sequence (0, 1, 1, 0, -1, -1)

G.f.: (1-x)^5/((1-x)^5-x); a(n)=sum{k=0..n, binomial(5n-4k-1,k)}; - Paul Barry, Feb 02 2006