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A113042 Number of solutions to +-p(1)+-p(2)+-...+-p(2n) = 3 where p(i) is the i-th prime. 5
0, 2, 1, 7, 15, 45, 139, 438, 1419, 4703, 16019, 55146, 190254, 671215, 2404179, 8534995, 30635448, 110495549, 401418693, 1467388464, 5393131894, 19883104535, 73856058401, 273600682457, 1017557492609, 3803885439979, 14266466901249, 53564801078049 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

+-p(1)+-p(2)+-...+-p(2n+1) = 3 does not have solutions, since the left hand side is even. [Corrected and edited by M. F. Hasler, Aug 09 2015]

LINKS

Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..1000 (first 120 terms from Alois P. Heinz)

MAPLE

A113042:=proc(n) local i, j, p, t; t:= NULL; for j from 2 to 2*n by 2 do p:=1; for i to j do p:=p*(x^(-ithprime(i))+x^(ithprime(i))); od; t:=t, coeff(p, x, 3); od; t; end;

# second Maple program

sp:= proc(n) sp(n):= `if`(n=0, 0, ithprime(n)+sp(n-1)) end:

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

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

     end:

a:= n-> b(3, 2*n):

seq(a(n), n=1..30);  # Alois P. Heinz, Aug 05 2012

MATHEMATICA

sp[n_] := sp[n] = If[n == 0, 0, Prime[n] + sp[n-1]]; b[n_, i_] := b[n, i] = If[n>sp[i], 0, If[i == 0, 1, b[n + Prime[i], i-1] + b[Abs[n - Prime[i]], i-1]]]; a[n_] := b[3, 2*n]; Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, Jan 31 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A022894 - A022904, A022920, A083309; A261061 - A261063 and A261045 (r.h.s. = -1); A261057, A261059, A261060 and A261044 (r.h.s. = -2); A113040, A113041.

Sequence in context: A239104 A260259 A141488 * A305881 A184346 A178622

Adjacent sequences:  A113039 A113040 A113041 * A113043 A113044 A113045

KEYWORD

nonn

AUTHOR

Floor van Lamoen, Oct 12 2005

STATUS

approved

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Last modified August 20 08:27 EDT 2019. Contains 326143 sequences. (Running on oeis4.)