The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334467 Square array read by antidiagonals upwards: T(n,k) is the sum of all parts of all partitions of n into consecutive parts that differ by k, with n >= 1, k >= 0. 1
 1, 4, 1, 6, 2, 1, 12, 6, 2, 1, 10, 4, 3, 2, 1, 24, 10, 8, 3, 2, 1, 14, 12, 5, 4, 3, 2, 1, 32, 14, 12, 10, 4, 3, 2, 1, 27, 8, 7, 6, 5, 4, 3, 2, 1, 40, 27, 16, 14, 12, 5, 4, 3, 2, 1, 22, 20, 18, 8, 7, 6, 5, 4, 3, 2, 1, 72, 22, 20, 18, 16, 14, 6, 5, 4, 3, 2, 1, 26, 24, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA T(n,k) = n*A323345(n,k). EXAMPLE Array begins: k 0 1 2 3 4 5 6 7 8 9 10 n +------------------------------------------------ 1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 2 | 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ... 3 | 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, ... 4 | 12, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, ... 5 | 10, 10, 5, 10, 5, 5, 5, 5, 5, 5, 5, ... 6 | 24, 12, 12, 6, 12, 6, 6, 6, 6, 6, 6, ... 7 | 14, 14, 7, 14, 7, 14, 7, 7, 7, 7, 7, ... 8 | 32, 8, 16, 8, 16, 8, 16, 8, 8, 8, 8, ... 9 | 27, 27, 18, 18, 9, 18, 9, 18, 9, 9, 9, ... 10 | 40, 20, 20, 10, 20, 20, 20, 10, 20, 10, 10, ... ... MATHEMATICA nmax = 13; col[k_] := col[k] = CoefficientList[Sum[x^(n(k n - k + 2)/2 - 1)/(1 - x^n), {n, 1, nmax}] + O[x]^nmax, x]; T[n_, k_] := n col[k][[n]]; Table[T[n-k, k], {n, 1, nmax}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Nov 30 2020 *) CROSSREFS Columns k: A038040 (k=0), A245579 (k=1), A060872 (k=2), A334463 (k=3), A327262 (k=4), A334733 (k=5), A334953 (k=6). Every diagonal starting with 1 gives A000027. Sequences of number of parts related to column k: A000203 (k=0), A204217 (k=1), A066839 (k=2) (conjectured), A330889 (k=3), A334464 (k=4), A334732 (k=5), A334949 (k=6). Sequences of number of partitions related to column k: A000005 (k=0), A001227 (k=1), A038548 (k=2), A117277 (k=3), A334461 (k=4), A334541 (k=5), A334948 (k=6). Polygonal numbers related to column k: A001477 (k=0), A000217 (k=1), A000290 (k=2), A000326 (k=3), A000384 (k=4), A000566 (k=5), A000567 (k=6). Cf. A245579, A323345, A334466. Sequence in context: A032145 A032050 A109915 * A255198 A202521 A247362 Adjacent sequences: A334464 A334465 A334466 * A334468 A334469 A334470 KEYWORD nonn,tabl AUTHOR Omar E. Pol, May 05 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 21 23:08 EDT 2023. Contains 361412 sequences. (Running on oeis4.)