A338431 Row length of irregular triangle A337939.

1, 1, 1, 3, 3, 4, 6, 10, 8, 13, 15, 15, 21, 26, 21, 36, 36, 33, 45, 49, 42, 64, 66, 58, 72, 89, 71, 99, 105, 80, 120, 136, 105, 151, 137, 129, 171, 188, 147, 190, 210, 165, 231, 247, 184, 274, 276, 228, 288, 295

Offset

1,4

Links

Table of n, a(n) for n=1..50.

Formula

a(1) = 1, and for n >= 2, a(n) = Sum_{k=1..floor(n/2)} k = A000217(floor(n/2)) if b(n) := floor(n/2) - delta(n) = A219839(n) = 0, where delta(n) = A055034(n), and if b(n) > 0, i.e., n = n(j) = A111774(j), for j >= 1, then a(n) < A000217(floor(n/2)), determined by a(n) = A000217(delta(n)) + R(n), with R(n) = Sum_{k = delta(n)+1..floor(n/2)} (1 + degree(S(k-1, x) evaluated with C(n, x) = 0)), where the C polynomial coefficients are given in A187360.

Example

n = 12: b(12) = 6 - 4 = 2 =  A219839(12) > 0, hence A000217(4) = 10,  R(4) = (1 + 2) + (1 + 1) = 5 from degree(S(4, x)/C(12,x) = 1*x^2) = 2 and degree(S(5, x)/C(12, x) = 2*x) = 1. Hence a(12) = 10 + 5 = 15.

Crossrefs

Cf. A000217, A055034, A219839, A337939.

Sequence in context: A363237 A080013 A152949 * A058660 A059871 A273096

Adjacent sequences: A338428 A338429 A338430 * A338432 A338433 A338434

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 15 2021

Status

approved