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 A168020 Square array read by antidiagonals in which row n lists the number of partitions of n into parts divisible by k. 8
 1, 2, 0, 3, 1, 0, 5, 0, 0, 0, 7, 2, 1, 0, 0, 11, 0, 0, 0, 0, 0, 15, 3, 0, 1, 0, 0, 0, 22, 0, 2, 0, 0, 0, 0, 0, 30, 5, 0, 0, 1, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 7, 3, 2, 0, 1, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 11, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 135, 0, 5, 0, 2, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In the square array, note that the column k starts with k-1 zeros. Then list each partition number of positive integers followed by k-1 zeros. See A000041, which is the main entry for this sequence. LINKS FORMULA a(n,k) = A000041(n/k) if k divides n; otherwise a(n,k) = 0. In particular, a(n,1) = a(n*k,k) = A000041(n). A000041(n) = number of partitions of (n*k) into parts divisible by k, for k>0. EXAMPLE The array begins: ================================================================ ..... Column k: 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 .10 .11 .12 Row .......................................................... .n ........................................................... =============================================================== ... 1 ....... ..1, .0, .0, .0, .0, .0, .0, .0, .0, .0, .0, .0, ... 2 ....... ..2, .1, .0, .0, .0, .0, .0, .0, .0, .0, .0, .0, ... 3 ....... ..3, .0, .1, .0, .0, .0, .0, .0, .0, .0, .0, .0, ... 4 ....... ..5, .2, .0, .1, .0, .0, .0, .0, .0, .0, .0, .0, ... 5 ....... ..7, .0, .0, .0, .1, .0, .0, .0, .0, .0, .0, .0, ... 6 ....... .11, .3, .2, .0, .0, .1, .0, .0, .0, .0, .0, .0, ... 7 ....... .15, .0, .0, .0, .0, .0, .1, .0, .0, .0, .0, .0, ... 8 ....... .22, .5, .0, .2, .0, .0, .0, .1, .0, .0, .0, .0, ... 9 ....... .30, .0, .3, .0, .0, .0, .0, .0, .1, .0, .0, .0, .. 10 ....... .42, .7, .0, .0, .2, .0, .0, .0, .0, .1, .0, .0, .. 11 ....... .56, .0, .0, .0, .0, .0, .0, .0, .0, .0, .1, .0, .. 12 ....... .77, 11, .5, .3, .0, .2, .0, .0, .0, .0, .0, .1, ... CROSSREFS Cf. A000041, A035377, A035444, A135010, A138121. Cf. A168016, A168017, A168018, A168019, A168021. [From Omar E. Pol, Nov 23 2009] Sequence in context: A202064 A144955 A225624 * A321878 A225084 A238345 Adjacent sequences:  A168017 A168018 A168019 * A168021 A168022 A168023 KEYWORD easy,nonn,tabl AUTHOR Omar E. Pol, Nov 20 2009 EXTENSIONS Edited by Omar E. Pol, Nov 21 2009 Edited by Charles R Greathouse IV, Mar 23 2010 Edited by Max Alekseyev, May 07 2010 STATUS approved

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Last modified October 16 06:24 EDT 2019. Contains 328049 sequences. (Running on oeis4.)