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A261062 Number of solutions to c(1)*prime(2) + ... + c(2n-1)*prime(2n) = -1, where c(i) = +-1 for i > 1, c(1) = 1. 3
0, 0, 1, 0, 6, 8, 30, 121, 385, 1102, 4207, 13263, 48904, 164298, 610450, 2108897, 7592564, 27444148, 100851443, 365507140, 1344593522, 4960584613, 18435632285, 68320148701, 254166868115, 951593812462, 3568369245595, 13386056545363, 50416752718382 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

There cannot be a solution for an even number of terms on the l.h.s. because all terms are odd but the r.h.s. is odd, too.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..300

EXAMPLE

a(1) = a(2) = 0 because prime(2) and prime(2) +- prime(3) +- prime(4) are always different from -1.

a(3) = 1 because the solution prime(2) + prime(3) - prime(4) + prime(5) - prime(6) = -1 is the only one involving prime(2) through prime(6).

MAPLE

s:= proc(n) option remember;

      `if`(n<3, 0, ithprime(n)+s(n-1))

    end:

b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=2, 1,

      b(abs(n-ithprime(i)), i-1)+b(n+ithprime(i), i-1)))

    end:

a:= n-> b(4, 2*n):

seq(a(n), n=1..30);  # Alois P. Heinz, Aug 08 2015

MATHEMATICA

s[n_] := s[n] = If[n < 3, 0, Prime[n] + s[n-1]];

b[n_, i_] := b[n, i] = If[n > s[i], 0, If[i == 2, 1, b[Abs[n-Prime[i]], i-1] + b[n+Prime[i], i-1]]];

a[n_] := b[4, 2n];

Array[a, 30] (* Jean-Fran├žois Alcover, Nov 07 2020, after Alois P. Heinz *)

PROG

(PARI) A261062(n, rhs=-1, firstprime=2)={rhs-=prime(firstprime); my(p=vector(2*n-2+bittest(rhs, 0), i, prime(i+firstprime))); sum(i=1, 2^#p-1, sum(j=1, #p, (-1)^bittest(i, j-1)*p[j])==rhs)} \\ For illustrative purpose; too slow for n >> 10.

CROSSREFS

Cf. A261061, A261063 and A261044 (starting with prime(1), prime(3) and prime(4)), A022894, ..., A022904, A022920, A083309 (r.h.s. = 0, 1 or 2), A261057, A261059, A261060, A261045 (r.h.s. = -2).

Sequence in context: A056097 A099431 A323201 * A076904 A354205 A219681

Adjacent sequences:  A261059 A261060 A261061 * A261063 A261064 A261065

KEYWORD

nonn

AUTHOR

M. F. Hasler, Aug 08 2015

EXTENSIONS

a(14)-a(29) from Alois P. Heinz, Aug 08 2015

STATUS

approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)