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Triangles Row Sum IntegerPartitions

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A008284 Triangle of partition numbers: T(n,k) = number of partitions of n in which the greatest part is k, 1<=k<=n. Also number of partitions of n into k positive parts, 1<=k<=n.

A026794 Triangular array T read by rows: T(n,k) = number of partitions of n in which least part is k, 1<=k<=n.

A049597 Triangular array T(n,k) in which k-th column gives coefficients of sum of Gaussian polynomials [k,m] for m=0..k.

A050314 Triangle: a(n,k) = number of partitions of n whose xor-sum is k.

A052249 Triangle T(n,k) (n >= 1, k >= 1) giving dimension of bigrading of Connes-Moscovici noncocommutative algebra.

A058398 Partition triangle A008284 read from right to left.

A072233 Square array T(n,k) read by antidiagonals giving number of ways to distribute n indistinguishable objects in k indistinguishable containers; containers may be left empty.

A091602 Triangle: T(n,k) = number of partitions of n such that some part is repeated k times and no part is repeated more than k times.

A096144 Triangle T(n,k) = number of partitions of n in which the least part occurs exactly k times, k=1..n.

A096771 Triangle read by rows: T(n,m) counts partitions of n that (just) fit inside an m X m box, but not in an (m-1) X (m-1) box. Partitions of n with Max(max part, length)= m.

A097364 Triangle read by rows, 0<=k<n: T(n,k) = number of partitions of n such that the differences between greatest and smallest parts are k.

A097567 T(n,k)= count of partitions p such that Abs( Odd(p)-Odd(p') ) = k, where p' is the transpose of p and Odd(p) counts the odd elements in p. Related to Stanley's 'f'.

A103919 Triangle of numbers of partitions of n with total number of odd parts equal to k from {0,...,n}.

A113685 Triangular array read by rows: T(n,k) is the number of partitions of n in which sum of odd parts is k, for k=0,1,...n; n>=0.

A113686 Triangular array T(n,k)=number of partitions of n in which sum of even parts is k, for k=0,1,...n; n>=0.

A114087 Triangle read by rows: T(n,k) is number of partitions of n whose tails below their Durfee squares have size k (n>=1; 0<=k<=n-1).

A114088 Triangle read by rows: T(n,k) is number of partitions of n whose tail below its Durfee square has k parts (n>=1; 0<=k<=n-1).

A115723 Table of partitions of n with maximum rectangle k.

A116598 Triangle read by rows: T(n,k) is the number of partitions of n having exactly k parts equal to 1 (n>=0, 0<=k<=n).

A116861 Triangle read by rows: T(n,k) is the number of partitions of n such that the sum of the parts, counted without multiplicities, is equal to k (n>=1, k>=1).

A118198 Triangle read by rows: T(n,k) is the number of partitions of n having k parts equal to the size of the Durfee square (0<=k<=n).

A124943 Table read by rows: number of partitions of n with k as low median.

A124944 Table, number of partitions of n with k as high median.

A130162 A051731 * A000837 as a diagonalized matrix.

A133121 Triangle T(n,k) read by rows = number of partitions of n such that number of parts minus number of distinct parts is equal to k, k = 0..n-1.

A134979 Triangle read by rows: T(n,k) = number of partitions of n where the maximum number of objects in partitions of any given size is k.

A135486 Triangle read by rows: T(n,k) = number of partitions of n having k-fold symmetry, cf. A085436.

A137586 Triangle read by rows: A026794 * A054525.

A161364 Triangle read by rows, modified version of A161363; row sums = A000041

A168532 Triangle read by rows, A054525 * A168021.

A174067 Triangle, row sums = A000041 starting (1, 2, 3, 5, 7,...); derived from finite differences of p(x) = A(x)*A(x^2) = B(x)*B(x^3) = C(x)*C(x^4) = ...

A174712 Triangle, right border = A000041, else zero; by rows, A000041(n) preceded by n zeros. By columns, n-th column = A000041(n) followed by zeros.

A175010 Triangle generated from INVERT transforms of variants of A080995; row sums = A000041 starting with offset 1.

A176202 Convolution triangle, row sums = A000041. M = A000041 in each column with two interleaved zeros; Q = A000726 diagonalized with the rest zeros. A176202 = M*Q.

A194799 Triangle read by rows: T(n,k) = number of partitions of n that are formed by k shells, k >= 1.

A209354 Triangular array: T(n,k) = number of partitions of n for which (maximal term)-(minimal term)=k, if 0<=k<n, and T(n,n)=1.

A215521 Number T(n,k) of distinct values of multinomial coefficients M(n;lambda), where lambda ranges over all partitions of n with largest part = k; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

A218907 Triangle, read by rows, of integer partitions of n by kernel size k.

A230025 Triangular array: t(n, k) = number of occurrences of k as the number of outliers in all the partitions of n.

A237513 Triangular array read by rows: T(n,k) = number of maximal horizontal rectangles that contain the Durfee square for partitions of n that consist of k nodes, 1 <= k <= n.

A238353 Triangle T(n,k) read by rows: T(n,k) is the number of partitions of n (as weakly ascending list of parts) with maximal ascent k, n >= 0, 0 <= k <= n.

A238354 Triangle T(n,k) read by rows: T(n,k) is the number of partitions of n (as weakly ascending list of parts) with minimal ascent k, n >= 0, 0 <= k <= n.

A243978 Triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) is the number of partitions of n where the minimal multiplicity of any part is k.

A259481 T(n,m) counts of border strips in skew tabloids of shape lambda/mu, with lambda and mu partitions of n and m (0<=m<=n).

A263233 Triangle read by rows: T(n,k) is the number of partitions of n having k perfect square parts (0<=k<=n).

A263234 Triangle read by rows: T(n,k) is the number of partitions of n having k triangular number parts (0<=k<=n).

A264391 Triangle read by rows: T(n,k) is the number of partitions of n having k perfect cube parts (0<=k<=n).

A264394 Triangle read by rows: T(n,k) is the number of partitions of n having k Mersenne number parts (0<=k<=n).

A264403 Triangle read by rows: T(n,k) is the number of partitions of n in which the sum of the parts of multiplicity 1 is equal to k (0<=k<=n).

A264405 Triangle read by rows: T(n,k) is the number of integer partitions of n having k repeated parts (each occurrence is counted).

A265247 Triangle read by rows: T(n,k) is the number of partitions of n in which the 2nd smallest part is k when the partition has at least 2 distinct parts and 0 otherwise; (n>=1, 0 <= k <= n).

A268189 Triangle read by rows: T(n,k) is the number of partitions of n for which the sum of the parts larger than the smallest part is k (n>=1, 0<=k<=n-1).