A111649 a(n) = A001541(n)*A001653(n+1) + A001541(n)*A002315(n) + A001653(n+1)*A002315(n).

3, 71, 2379, 80783, 2744211, 93222359, 3166815963, 107578520351, 3654502875939, 124145519261543, 4217293152016491, 143263821649299119, 4866752642924153523, 165326326037771920631, 5616228332641321147899

Offset

0,1

Links

Ray Chandler, Table of n, a(n) for n = 0..652

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

a(n) = A001653(2n+2) - 2*A002315(n)^2, e.g., 2379 = 5741 - 2*41^2;

a(n) = A001652(2n) + A002315(n)^2 + 2, e.g., 2379 = 696 + 41^2 + 2;

a(n) = 2*A046176(n+1)+1, e.g., 2379 = 2*1189 + 1.

G.f.: (x^2+34*x-3) / ((x-1)*(x^2-34*x+1)). - Colin Barker, Dec 14 2014 [adjusted for corrected term and empirical g.f. confirmed for more terms and recurrence of source sequences. - Ray Chandler, Feb 05 2024]

Example

a(1) = 71 = 3*5 + 3*7 + 5*7.

Mathematica

LinearRecurrence[{35, -35, 1}, {3, 71, 2379}, 20] (* Paolo Xausa, Feb 06 2024 *)

Crossrefs

Cf. A001541, A001653, A002315, A111647, A111648.

Sequence in context: A166449 A094458 A183548 * A349072 A272657 A226709

Adjacent sequences: A111646 A111647 A111648 * A111650 A111651 A111652

Keyword

nonn

Author

Charlie Marion, Aug 24 2005

Extensions

a(3) = 80783 corrected by Ray Chandler, Feb 05 2024

Status

approved