A292994 Number of integers m, 1 <= m <= A002569(n), that are not terms in the triangle T(n,k) of A008284.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 6, 8, 12, 19, 26, 39, 52, 71, 92, 120, 161, 205, 258, 320, 398, 499, 613, 754, 911, 1103, 1340, 1622, 1956, 2338, 2789, 3303, 3938, 4690, 5547, 6551, 7690, 9018, 10584, 12425, 14559, 16989, 19790, 22970, 26615

Offset

1,13

Links

Table of n, a(n) for n=1..53.

Example

With n = 10, the maximum value of m is 9 and all values of m from 1 to 9 appear within the first 10 rows of A008284, so a(10) = 0.
With n = 13, the maximum value of m is 18 and all values of m from 1 to 18, except 16 and 17, appear within the first 13 rows of A008284, so a(13) = 2.

Mathematica

FoldList[{#1, Count[Range@ Max@ #2, k_ /; FreeQ[#1, k]]} & @@ {Append[#1, #2], #2} & @@ {First@ #1, Table[SeriesCoefficient[1/QPochhammer[a q, q], {q, 0, #2}, {a, 0, k}], {k, #2}]} &, {{{1}}, 0}, Range[2, 40]][[All, -1]] (* Michael De Vlieger, Sep 29 2017, after Vladimir Reshetnikov at A008284 *)

Crossrefs

Cf. A008284, A002569.

Sequence in context: A324939 A057335 A126907 * A323114 A362231 A118563

Adjacent sequences: A292991 A292992 A292993 * A292995 A292996 A292997

Keyword

nonn

Author

J. Stauduhar, Sep 28 2017

Status

approved