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

Author

Wolfdieter Lang, Jan 15 2021

Keywords

• nonn
• easy

Examples

			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.

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.