31501

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=20A006053
• A036827/2.at n=7A036828
• Third row of Pascal-(1,5,1) array A081580.at n=42A081589
• Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 7 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2*n, s(0) = 1, s(2n) = 3.at n=9A094790
• a(n) = a(n-1) + Sum_{k=0..n/3} a(n-3k) with a(0)=1.at n=25A113435
• Second row of A113435.at n=8A113437
• a(n) = 900*n + 1.at n=34A158407
• a(n) = 109*n^2.at n=17A174339
• 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=41A187065
• 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=39A187066
• 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=38A187067
• Number of partitions p of n such that the number of numbers having multiplicity 1 in p is a part or the number of numbers having multiplicity > 1 is a part.at n=40A239737
• Expansion of g.f. (1-2*x+51*x^2)/(1-x)^3.at n=36A257352
• 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=40A265755
• T(n,k) = Number of n X k arrays containing k copies of 0..n-1 with no element 1 greater than its north or southwest neighbor modulo n and the upper left element equal to 0.at n=24A266861
• Number of 4Xn arrays containing n copies of 0..4-1 with no element 1 greater than its north or southwest neighbor modulo 4 and the upper left element equal to 0.at n=3A266863
• T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element 1 greater than its west or northeast neighbor modulo n and the upper left element equal to 0.at n=24A266867
• Number of 4Xn arrays containing n copies of 0..4-1 with no element 1 greater than its west or northeast neighbor modulo 4 and the upper left element equal to 0.at n=3A266869
• Number of integer partitions of n whose run-lengths are neither weakly increasing nor weakly decreasing.at n=42A332641