A087098 -id:A087098 - 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

A087099 Partial sums of A063914.

Original entry on oeis.org

1, 3, 6, 11, 16, 24, 31, 42, 51, 65, 76, 93, 106, 126, 141, 164, 181, 207, 226, 255, 276, 308, 331, 366, 391, 429, 456, 497, 526, 570, 601, 648, 681, 731, 766, 819, 856, 912, 951, 1010, 1051, 1113, 1156, 1221, 1266, 1334, 1381, 1452, 1501, 1575, 1626

Offset: 1

Jeremy Gardiner, Aug 10 2003

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A086848, A087098, A001068.

With[{nn=50},Accumulate[Riffle[Range[1,2*nn,2],3*Range[0,nn]+2]]] (* Harvey P. Dale, Jul 25 2013 *)

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

A087100 A000225 (2^n - 1) interlaced with A008593 (11n).

Original entry on oeis.org

0, 1, 11, 3, 22, 7, 33, 15, 44, 31, 55, 63, 66, 127, 77, 255, 88, 511, 99, 1023, 110, 2047, 121, 4095, 132, 8191, 143, 16383, 154, 32767, 165, 65535, 176, 131071, 187, 262143, 198, 524287, 209, 1048575, 220, 2097151, 231, 4194303, 242, 8388607, 253

Offset: 0

Jeremy Gardiner, Aug 10 2003

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-5,0,2).

Cf. A063914, A087098, A086848.

Rest[With[{nn=30},Riffle[2^Range[0,nn]-1,11Range[0,nn]]]] (* Harvey P. Dale, Aug 15 2011 *)

From Chai Wah Wu, Feb 02 2021: (Start)
a(n) = 4*a(n-2) - 5*a(n-4) + 2*a(n-6) for n > 5.
G.f.: x*(22*x^3 + x^2 - 11*x - 1)/((x - 1)^2*(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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A087099 Partial sums of A063914.

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A087100 A000225 (2^n - 1) interlaced with A008593 (11n).

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