A092121 Minimum sum of absolute values of coefficients of a product of n binomials.

6, 8, 10, 12, 16, 16, 20, 24, 28

Offset

3,1

Comments

Consider polynomials of the form P(a_1, ..., a_n) = (1-x^{a_1})*...*(1-x^{a_n}), where a_i are positive integers. Let L(a_1, ..., a_n) be the sum of absolute values of the coefficients. Then a(n) = min { L(a_1, ..., a_n) : 1 <= a_1 <= ..., <= a_n }.

Upper bounds (probably not tight, except perhaps for a(12)) for the following terms are: 36, 44, 52, 52, 60, 68, 84, 96, 116, 130, 140, 156, 192, 188, 228, 262, 280, 316, 368, 344, 416, 440, 460, 456, 492, 584, 652, 688, 684, 734, 872, 902, 976, 988, 1136, 1176, 1224, 1328, 1448, 1632, 1544, 1596, 1712, 1728, 1840.

Links

Table of n, a(n) for n=3..11.

P. Borwein and C. Ingalls, The Prouhet-Tarry-Escott problem revisited, L'Enseign. Math., 40 (1994), pp. 3-27.

M. Cipu, Upper bounds for norms of products of binomials, LMS J. Comput. Math., 7 (2004), pp. 37-49.

R. Maltby, Pure product polynomials and the Prouhet-Tarry-Escott problem, Math. Comp., 66 (1966), pp. 1323-1340.

Crossrefs

Sequence in context: A075396 A269135 A369666 * A005525 A023385 A315850

Adjacent sequences: A092118 A092119 A092120 * A092122 A092123 A092124

Keyword

nonn,more

Author

Mihai Cipu (mihai.cipu(AT)imar.ro), Mar 30 2004

Status

approved