35002

Appears in sequences

• Generating function = Product_{m>=1} 1/(1 - x^m)^2; a(n) = number of partitions of n into parts of 2 kinds.at n=21A000712
• Divide n-th row of A084024 by n.at n=18A084025
• Number of partitions of 2*n + 1 into parts of two kinds.at n=10A100535
• Triangle read by rows: T(n,k) = 3*T(n-1,k-1) + 3*T(n-1,k) - 2*T(n-2,k-1) with T(n,0) = T(n,n) = 1.at n=39A152613
• Triangle read by rows: T(n,k) = 3*T(n-1,k-1) + 3*T(n-1,k) - 2*T(n-2,k-1) with T(n,0) = T(n,n) = 1.at n=41A152613
• a(n) is the number of patterns for n-digit papaya numbers.at n=13A165136
• a(n) is the number of patterns for n-character papaya words in an infinite alphabet.at n=14A165137
• Number of n X 3 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.at n=5A281883
• Number of nX6 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.at n=2A281886
• T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.at n=30A281888
• T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.at n=33A281888
• a(n) = strictly increasing number m, such that m+n is the next prime and m-n is the previous prime.at n=20A282687
• E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + x * A(x)) ).at n=5A372178