A086848 First differences are formed by interleaving {2^k - 1, k = 1, 2, 3, ...} and {11*k, k = 5, 4, 3, ...}.

42, 43, 98, 101, 145, 152, 185, 200, 222, 253, 264, 327, 327, 454, 443, 698, 676, 1187, 1154, 2177, 2133, 4180, 4125, 8220, 8154, 16345, 16268, 32651, 32563, 65330, 65231, 130766, 130656, 261727, 261606, 523749, 523617, 1047904

Offset: 1

Author

Michael M. Taylor, Aug 09 2003

Keywords

• nonn

Comments

A version of this was given as a puzzle somewhere.

There are infinitely many solutions to the stated sequence name producing the specified interleaving as a first difference. I assume there was some other condition given in the puzzle that arrived at this particular solution. - Ray Chandler, May 07 2025

Links

• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-5,5,2,-2).

Crossrefs

Cf. A087098, A087099, A001068.

Formula

Empirical g.f.: x*(48*x^6+34*x^4-x^3-113*x^2+x+42) / ((x-1)^3*(x+1)^2*(2*x^2-1)). - Colin Barker, Mar 05 2013

Conjectured g.f. above confirmed. Interleaving of two linear recurrences is another linear recurrence, as is the first difference. - Ray Chandler, May 07 2025