A270708 a(n) = A048739(n-1) mod A000129(floor(n/2)).

0, 0, 0, 1, 4, 3, 0, 1, 28, 27, 0, 1, 168, 167, 0, 1, 984, 983, 0, 1, 5740, 5739, 0, 1, 33460, 33459, 0, 1, 195024, 195023, 0, 1, 1136688, 1136687, 0, 1, 6625108, 6625107, 0, 1, 38613964, 38613963, 0, 1, 225058680, 225058679, 0, 1, 1311738120, 1311738119, 0, 1, 7645370044, 7645370043, 0, 1

Offset: 2

Author

Altug Alkan, Mar 22 2016

Keywords

• nonn

Comments

It appears that a(4*n+1) = 1. - Michel Marcus, Mar 23 2016

Examples

			a(7) = 3 because a(7) = A048739(6) mod A000129(floor(7/2)) = (1 + 2 + 5 + 12 + 29 + 70 + 169) mod 5 = 288 mod 5 = 3.
a(8) = 0 because a(8) = A048739(7) mod A000129(floor(8/2)) = (1 + 2 + 5 + 12 + 29 + 70 + 169 + 408) mod 12 = 0.
a(9) = 1 because a(9) = A048739(8) mod A000129(floor(9/2)) = (1 + 2 + 5 + 12 + 29 + 70 + 169 + 408 + 985) mod 12 = 1.
		

Crossrefs

Cf. A000129 (Pell numbers), A048739 (partial sums of Pell numbers).

Programs

PARI

a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
for(n=2, 1e2, print1(sum(k=1, n, a000129(k)) % a000129(n\2),", "));

Formula

Empirical g.f.: x^5*(1+3*x-6*x^4+6*x^5+x^8-x^9) / ((1-x)*(1+x^2)*(1+2*x^2-x^4)*(1-2*x^2-x^4)). - Colin Barker, Mar 22 2016