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 A330888 Irregular triangle read by rows: T(n,k) is the number of parts in the partition of n into k consecutive parts that differ by 3, n >= 1, k >= 1, and the first element of column k is in the row that is the k-th pentagonal number (A000326). 10
 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 3, 1, 2, 0, 1, 0, 0, 1, 2, 3, 1, 0, 0, 1, 2, 0, 1, 0, 3, 1, 2, 0, 1, 0, 0, 1, 2, 3, 1, 0, 0, 4, 1, 2, 0, 0, 1, 0, 3, 0, 1, 2, 0, 0, 1, 0, 0, 4, 1, 2, 3, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 4, 1, 2, 0, 0, 1, 0, 0, 0, 1, 2, 3, 0, 1, 0, 0, 4, 1, 2, 0, 0, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Since the trivial partition n is counted, so T(n,1) = 1. This is an irregular triangle read by rows: T(n,k), n >= 1, k >= 1, in which column k lists k's interleaved with k-1 zeros, and the first element of column k is in the row that is the k-th pentagonal number. LINKS FORMULA T(n,k) = k*A330887(n,k). EXAMPLE Triangle begins (rows 1..26): 1; 1; 1; 1; 1, 2; 1, 0; 1, 2; 1, 0; 1, 2; 1, 0; 1, 2; 1, 0, 3; 1, 2, 0; 1, 0, 0; 1, 2, 3; 1, 0, 0; 1, 2, 0; 1, 0, 3; 1, 2, 0; 1, 0, 0; 1, 2, 3; 1, 0, 0, 4; 1, 2, 0, 0; 1, 0, 3, 0; 1, 2, 0, 0; 1, 0, 0, 4; ... For n = 21 there are three partitions of 21 into consecutive parts that differ by 3, including 21 as a partition. They are [21], [12, 9] and [10, 7, 4]. The number of parts of these partitions are 1, 2 and 3 respectively, so the 21st row of the triangle is [1, 2, 3]. MAPLE A330888 := proc(n, k)     k*A330887(n, k) ; end proc: for n from 1 to 40 do     for k from 1 do         if n>= A000325(k) then             printf("%d, ", A330888(n, k)) ;         else             break;         end if;     end do:     printf("\n") ; end do: # R. J. Mathar, Oct 02 2020 CROSSREFS Cf. A000326, A330887. Other triangles of the same family are A127093, A285914, A330466. Sequence in context: A054848 A284171 A286320 * A194525 A330466 A282938 Adjacent sequences:  A330885 A330886 A330887 * A330889 A330890 A330891 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 30 2020 STATUS approved

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)