A360431 a(n) is the smallest positive integer which can be represented as the sum of n distinct binomial coefficients binomial(k,n) for some k >= n in exactly n ways, or -1 if no such integer exists.

1, 16, 305, 4396, 43093, 332193, 87172020, 273879343

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Binomial Coefficient

Example

For n = 2: 16 = C(2,2) + C(6,2) = C(4,2) + C(5,2) = 1 + 15 = 6 + 10.
For n = 3: 305 = C(3,3) + C(9,3) + C(12,3) = C(6,3) + C(10,3) + C(11,3) = C(8,3) + C(9,3) + C(11,3) = 1 + 84 + 220 = 20 + 120 + 165 = 56 + 84 + 165.
For n = 4: 4396 = C(5,4) + C(11,4) + C(14,4) + C(18,4) = C(8,4) + C(9,4) + C(16,4) + C(17,4) = C(9,4) + C(12,4) + C(13,4) + C(18,4) = C(10,4) + C(14,4) + C(15,4) + C(16,4) = 5 + 330 + 1001 + 3060 = 70 + 126 + 1820 + 2380 = 126 + 495 + 715 + 3060 = 210 + 1001 + 1365 + 1820.

Crossrefs

Cf. A007318, A350288, A360217.

Sequence in context: A253302 A227678 A252863 * A039746 A232834 A232841

Adjacent sequences: A360428 A360429 A360430 * A360432 A360433 A360434

Keyword

nonn,more

Author

Ilya Gutkovskiy, Feb 07 2023

Extensions

a(8) from Michael S. Branicky, Feb 17 2023

Status

approved