t is the first...: A005224 *
T-coordinates for arrays: (01) sequences related to (start):
T-coordinates for arrays: (02) The usual coordinates for a triangular array are are T(n,k), with n >= 0 and 0 <= k <= n, as follows:
T-coordinates for arrays: (03) .............T(0,0)
T-coordinates for arrays: (04) .........T(1,0) T(1,1)
T-coordinates for arrays: (05) ......T(2,0) T(2,1) T(2,2)
T-coordinates for arrays: (06) ...T(3,0) T(3,1) T(3,2) T(3,3)
T-coordinates for arrays: (07) ................................
T-coordinates for arrays: (08) with associated generating function T(x,y) = Sum_{n >= 0, 0 <= k <= n} T(n,k) x^n y^k.
T-coordinates for arrays: (09) Sometimes it is more convenient to relabel the entries using U-coordinates U(i,j), i >= 0, j >= 0, i+j = n, as follows:
T-coordinates for arrays: (10) .............U(0,0)
T-coordinates for arrays: (11) .........U(1,0) U(0,1)
T-coordinates for arrays: (12) ......U(2,0) U(1,1) U(0,2)
T-coordinates for arrays: (13) ...U(3,0) U(2,1) U(1,2) U(0,3)
T-coordinates for arrays: (14) ................................
T-coordinates for arrays: (15) with associated generating function U(z,w) = Sum_{i >= 0, j >= 0} U(i,j) z^i w^j.
T-coordinates for arrays: (16) Of course U(x,y) = T(x, y/x), T(x,y) = U(x,xy).
T-coordinates for arrays: (17) E.g. for Pascal's triangle A007318 with T(n,k) = binomial(n,k) we have T(x,y) = 1/(1-x*(1+y)), U(z,w) = 1/(1-z-w), the latter being rather nicer.
t-designs, spherical: see spherical designs
table (or triangle) , sequences related to (start):
table (or triangle) of (1): x+y (A003056 *), |x-y| (A049581 *), xy (A003991 *, A004247 *), [x/y] (A003988 *), x^y (A003992 *, A004248 *, A051128 *, A051129 *), max(x,y) (A003984 *, A051125 *)
table (or triangle) of (2): min(x,y) (A003983 *, A004197 *), x mod y (A051126 *, A051127 *), GCD(x,y) (A003989 *, A050873 *), LCM(x,y) (A003990 *, A051173 *), x OR y (A003986 *), x XOR y (A003987 *), x AND y (A004198 *)
table (or triangle) of (3): x divisible by y (A051731 *), phi(x/y) (A054523 ), Moebius(x/y) (A054525 )
table: graphs by numbers of nodes and edges: A008406
take 1, skip 2, etc.: A007606 , A007607
take-a-factorial: A014587 *
take-a-Fibonacci-number: A014588 *
take-a-prime: A014589 *
take-a-square: A014586 *
take-a-triangle: A019509 *
tan(x), Taylor series for: A000182 *, A002430 */A036279 *
tan(x): see also A000111 , A007314 , A006229 , A001469 , A003716 , A003705 , A003706 , A003707 , A003708 , A003718 , A003719 , A003720 , A003710 , A003721 , A003700 , A003702
tangent numbers , sequences related to (start):
tangent numbers, A000182 *
tangent numbers, generalized:: A000061 , A000176 , A002302 , A000191 , A000318 , A000320 , A000411 , A000464 , A002303 , A000488 , A005801 , A000518
tangent numbers, triangle of: A008308 *
tangent numbers: see also A007314
tangrams: A006074
tanh(x), Taylor series for: A000182 *, A002430 */A036279 *
tanh(x): see also A003711 , A003717 , A003721 , A003723
tatami mats: A000930 , A052270
tau(n), number of divisors: A000005 *
tau(n), number of divisors: records: A002183 , A002182
tau: see also golden ratio phi
tau_k or d_k numbers, number of ordered n-factorizations of n: (for explicit formula see A007425 ). Table by antidiagonals A077592 ; for k=1..11 see A000012 , A000005 , A007425 , A007426 , A061200 , A034695 , A111217 , A111218 , A111219 , A111220 , A111221 .
taxi-cab numbers: A001235 *, A011541 *, A023050 *, A023051 , A003826 , A047696
taxicab numbers: see taxi-cab numbers
Tchebycheff is spelled Chebyshev throughout
Tchebychev is spelled Chebyshev throughout
Tchoukaillon (or Mancala) solitaire: A028932 * (the main entry), A002491 , A007952 , A028920 *, A028931 , A028933