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