49612

Appears in sequences

• Triangle read by rows: T(n,k) is the number of weighted lattice paths in L_n having k peaks.The members of L_n are paths of weight n that start at (0,0), end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A peak is a (1,1)-step followed by a (1,-1)-step.at n=40A182903
• Number of weighted lattice paths in L_n having no peaks. The members of L_n are paths of weight n that start at (0,0), end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A peak is a (1,1)-step followed by a (1,-1)-step.at n=14A182904
• Number of partitions of n for which 2*(number of distinct parts) <= (number of parts).at n=44A237363
• a(n) is the Pisano period of prime(n)^2.at n=36A343116
• Long legs of the only primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.at n=36A367573