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Index to OEIS: Section Ta

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Index to OEIS: Section Ta


[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]


t is the first...: A005224*
T-coordinates for arrays: (01) sequences related to :

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-core partitions: see core partitions
t-designs, spherical: see spherical designs
table (or triangle) , sequences related to :

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 :

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, A068920, A068923, A068924, A068925, A068927, A068928, A068929
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*, A018850*, 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


[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]


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