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A113042
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Number of solutions to +-p(1)+-p(2)+-...+-p(2n) = 3 where p(i) is the i-th prime.
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5
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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
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OFFSET
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1,2
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COMMENTS
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+-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]
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LINKS
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FORMULA
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a(n) = [x^3] Product_{k=1..2*n} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 30 2024
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MAPLE
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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):
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MATHEMATICA
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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-François Alcover, Jan 31 2017, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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