74305

Appears in sequences

• Largest triangular number less than or equal to sum of previous terms with a(0)=1.at n=18A061883
• Terms of A073872 that do not change their position in the rearrangement; i.e., values of A073872(n) which equal n(n+1)/2.at n=31A073873
• Triangular numbers with square pyramidal indices.at n=10A076767
• a(n) = A000217(A000041(n)).at n=18A086737
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.at n=10A149845
• Number of ways to place zero or more nonadjacent 1,0 1,1 2,1 2,2 3,1 polyhexes in any orientation on a planar nXnXn triangular grid.at n=7A155227
• 1/16 the number of (n+1) X 2 0..3 arrays with all 2 X 2 subblocks having the same four values.at n=13A184031
• a(n) = m*(m+1)/2, where m = floor(n^(3/2)).at n=52A185541
• E.g.f. satisfies: A(x) = 1 + A(x)^4 * Integral 1/A(x) dx.at n=5A234292
• a(0)=0, a(1)=a(2)=a(3)=a(4)=1; thereafter, a(n) = Sum_{k=1..5} a(n-k-(a(n-k) mod 5)).at n=31A259615
• Hexagonal numbers (A000384) in which parity of digits alternates.at n=19A297645
• The first of two consecutive triangular numbers the sum of which is equal to the sum of two consecutive prime numbers.at n=24A298462
• Total number of parts in all symmetric m-color cyclic compositions of n (that is, the total number of parts in all achiral cyclic compositions of n where a part with size m can be colored with one of m colors).at n=16A307415
• Terms of A324315 (squarefree integers m > 1 such that if prime p divides m, then the sum of the base p digits of m is at least p) that are also hexagonal numbers (A000384) with index equal to their largest prime factor.at n=11A324319
• Intersection of A099011 and A327651.at n=35A327652
• Number of (i,j,k) in {1,2,...,n}^3 such that gcd(n,i) = gcd(n,j) = gcd(n,k).at n=48A338997
• Hexagonal numbers that are products of exactly four distinct primes.at n=33A381920