30381

Appears in sequences

• 2nd elementary symmetric function of the first n+1 positive integers congruent to 2 mod 3.at n=11A024391
• G.f.: 1/((1-x)*(1-x^2))^6.at n=10A038166
• Expansion of (1+15*x+15*x^2+x^3)/(1-x)^12.at n=5A059603
• Smallest triangular number which is a multiple (>1) of the n-th triangular number.at n=37A068084
• Numbers k such that k and 10*k are both triangular numbers.at n=5A068085
• Triangular numbers with sum of digits = 15.at n=34A068130
• Triangular numbers with property that digits alternate in parity.at n=34A068882
• Triangular numbers with property that digits alternate in parity individually as well as in concatenation with previous terms.at n=18A068889
• Largest coefficient in expansion of (1 + x + x^2 + ... + x^(n-1))^5 = ((1-x^n)/(1-x))^5, i.e., the coefficient of x^floor(5*(n-1)/2) and of x^ceiling(5*(n-1)/2); also number of compositions of floor(5*(n+1)/2) into exactly 5 positive integers each no more than n.at n=15A077044
• a(n) = n*(n - 1)*(n + 2)/2.at n=38A077414
• Number of ordered quintuples (a,b,c,d,e), -n <= a,b,c,d,e <= n, such that a+b+c+d+e = 0.at n=7A083669
• Triangular numbers t such that t+10 is a prime.at n=32A129755
• 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, 0, -1), (0, -1, 0), (1, 0, 0), (1, 1, 1)}.at n=8A150492
• a(n) = n*(n+1)*(3*n^2+5*n+4)/12.at n=18A176060
• 41 times triangular numbers.at n=38A195038
• Number of arrays of n integers in -7..7 with sum zero.at n=5A201551
• Number of all possible tetrahedra of any size, having reverse orientation to the original regular tetrahedron, formed when intersecting the latter by planes parallel to its sides and dividing its edges into n equal parts.at n=37A216172
• Least triangular number of the form p*triangular(n) where p is a prime number, or 0 if no such triangular number exists.at n=38A225789
• Triangular numbers T such that both (T+2) and (T-2) are semiprimes.at n=35A242356
• Triangular numbers that are the product of a triangular number and a prime number.at n=45A253651