A087099 -id:A087099 - cp's OEIS frontend

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

Michael M. Taylor, Aug 09 2003

nonn

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

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

Cf. A087098, A087099, A001068.

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

A087098 Partial sums of A087100.

Original entry on oeis.org

0, 1, 12, 15, 37, 44, 77, 92, 136, 167, 222, 285, 351, 478, 555, 810, 898, 1409, 1508, 2531, 2641, 4688, 4809, 8904, 9036, 17227, 17370, 33753, 33907, 66674, 66839, 132374, 132550, 263621, 263808, 525951, 526149, 1050436, 1050645, 2099220

Offset: 0

Jeremy Gardiner, Aug 10 2003

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

Cf. A086848, A087099, A001068.

Accumulate[Rest[With[{nn=30},Riffle[2^Range[0,nn]-1,11Range[0,nn]]]]] (* Harvey P. Dale, Feb 13 2017 *)

From Chai Wah Wu, Feb 02 2021: (Start)
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 5*a(n-4) + 5*a(n-5) + 2*a(n-6) - 2*a(n-7) for n > 6.
G.f.: x*(-22*x^3 - x^2 + 11*x + 1)/((x - 1)^3*(x + 1)^2*(2*x^2 - 1)). (End)

cp's OEIS Frontend

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

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