A369733 Number of solutions to 2*k_1 + 3*k_2 + ... + prime(n)*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

0, 0, 1, 1, 3, 8, 18, 39, 95, 233, 565, 1440, 3640, 9409, 24957, 66699, 177931, 475584, 1292985, 3517163, 9636135, 26675682, 73847316, 205379443, 571621138, 1588186858, 4435778209, 12474517743, 35194193531, 99781874834, 283513309423, 799779819641

Offset

0,5

Links

Table of n, a(n) for n=0..31.

Formula

a(n) = [x^1] Product_{k=1..n} (x^prime(k) + 1 + 1/x^prime(k)).

Maple

s:= proc(n) s(n):= `if`(n<1, 0, ithprime(n)+s(n-1)) end:
b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=0, 1,
      b(n, i-1)+b(n+ithprime(i), i-1)+b(abs(n-ithprime(i)), i-1)))
    end:
a:= n-> b(1, n):
seq(a(n), n=0..32);  # Alois P. Heinz, Jan 30 2024

Mathematica

Table[Coefficient[Product[(x^Prime[k] + 1 + 1/x^Prime[k]), {k, 1, n}], x, 1], {n, 0, 31}]

Crossrefs

Cf. A007576, A063866, A113040, A350880, A369560, A369628.

Sequence in context: A317188 A360784 A335464 * A026635 A135094 A026657

Adjacent sequences: A369730 A369731 A369732 * A369734 A369735 A369736

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2024

Status

approved