56714

Appears in sequences

• a(n) = a(n-1) + 2*a(n-2) - a(n-3), with a(0) = a(1) = 0, a(2) = 1.at n=21A006053
• Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 7 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n+1, s(0) = 1, s(2n+1) = 4.at n=9A094789
• a(n)=5a(n-1)-11a(n-2)+13a(n-3)-9a(n-4)+3a(n-5)-a(n-6).at n=21A140342
• Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n=2*r+p_i, and define a(-2)=1. Then, a(n)=a(2*r+p_i) gives the quantity of H_(7,1,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt(2*cos(Pi/7)).at n=43A187065
• Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n=2*r+p_i, and define a(-2)=0. Then, a(n)=a(2*r+p_i) gives the quantity of H_(7,2,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt(2*cos(Pi/7)).at n=41A187066
• Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n = 2*r + p_i and define a(-2)=0. Then, a(n) = a(2*r + p_i) gives the quantity of H_(7,3,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x = sqrt(2*cos(Pi/7)).at n=40A187067
• a(n) = a(n-1) + a(n-2) if n is even and a(n) = a(n-3) + a(n-4) if n is odd, with a(0) = a(1) = a(2) = 0 and a(3) = 1.at n=42A265755
• E.g.f.: -sinh(x)*LambertW(-x).at n=7A277476
• G.f.: Sum_{n>=0} (3 + (1+x)^n)^n / (4 + (1+x)^n)^(n+1).at n=5A302615
• Numbers that are the sum of ten fifth powers in three or more ways.at n=25A345635
• Numbers that are the sum of ten fifth powers in exactly three ways.at n=21A346348