V. T. Jayabalaji - cp's OEIS frontend

A226649 Fibonacci shuffles: a(2n) = A000071(n) and a(2n+1) = A001611(n+2).

0, 2, 0, 3, 1, 4, 2, 6, 4, 9, 7, 14, 12, 22, 20, 35, 33, 56, 54, 90, 88, 145, 143, 234, 232, 378, 376, 611, 609, 988, 986, 1598, 1596, 2585, 2583, 4182, 4180, 6766, 6764, 10947, 10945, 17712, 17710, 28658, 28656, 46369, 46367, 75026, 75024, 121394, 121392, 196419, 196417, 317812, 317810

Offset: 0

V. T. Jayabalaji, Jun 14 2013

a(2*n+1) = a(2*n) + A157725(n); a(2*n) = a(2*n-1) - 2 for n > 0. - Reinhard Zumkeller, Jul 30 2013

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1,1,1).

Cf. A000071, A001611, A096748.

import Data.List (transpose)
a226649 n = a226649_list !! n
a226649_list = concat $ transpose [a000071_list, drop 2 a001611_list]
-- Reinhard Zumkeller, Jul 30 2013

LinearRecurrence[{-1,1,1,1,1},{0,2,0,3,1},60] (* Harvey P. Dale, Sep 12 2018 *)

G.f. -x*(2+x^2+2*x^3+2*x) / ( (1+x)*(x^4+x^2-1) ). - R. J. Mathar, Jul 15 2013
a(n) + a(n+1) = A096748(n+2). - R. J. Mathar, Jul 15 2013
a(2n-1) - 1 = a(2n) + 1 = fib(n+1) = A000045(n+1) for n > 0. - T. D. Noe, Jul 23 2013

A227393 a(n) = concatenation of first 3n terms of A033627.

Original entry on oeis.org

1, 124, 12471013, 12471013161922, 12471013161922252831, 124710131619222252831343740, 124710131619222252831343740434649, 124710131619222252831343740434649525558

Offset: 1

V. T. Jayabalaji, Jul 15 2013

All entries are == 1 (mod 3). V. T. Jayabalaji, Jul 13 2013

			124 is the concatenation of 1,2 and 4.
12471013 is the concatenation of 1, 2, 4, 7 10 and 13.

Cf. A033627

Edited by N. J. A. Sloane, Jul 16 2013

A226538 a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 7, 11, 12, 19, 20, 32, 33, 53, 54, 87, 88, 142, 143, 231, 232, 375, 376, 608, 609, 985, 986, 1595, 1596, 2582, 2583, 4179, 4180, 6763, 6764, 10944, 10945, 17709, 17710, 28655, 28656, 46366, 46367, 75023, 75024, 121391, 121392, 196416, 196417

Offset: 0

V. T. Jayabalaji, Jun 10 2013

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,-1).

a226538 n = a226538_list !! n
a226538_list = concat $ transpose [drop 2 a000071_list, tail a001911_list]
-- Reinhard Zumkeller, Jun 18 2013

f:= proc(n) option remember;
      if n <= 1 then 1
    elif n mod 2 = 0 then f(n-1)+1
    else f(n-1)+f(n-3)
      fi
    end:
t21:=[seq(f(n),n=0..60)];

LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 2, 3, 4, 6}, 50] (* Jean-François Alcover, Feb 13 2018 *)

a(2n) = A000071(n+3), a(2n+1) = A001911(n+1). - Philippe Deléham, Jun 18 2013
G.f.: (1+x+x^3)/((1-x)*(1+x)*(1-x^2-x^4)). - Philippe Deléham, Jun 18 2013
a(n) = a(n-1) + a(n-3)*(1-(-1)^n)/2 + (1+(-1)^n)/2. - Paolo P. Lava, Jun 27 2013

Edited by N. J. A. Sloane, Jun 18 2013

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User: V. T. Jayabalaji

A226649 Fibonacci shuffles: a(2n) = A000071(n) and a(2n+1) = A001611(n+2).

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A227393 a(n) = concatenation of first 3n terms of A033627.

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A226538 a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.

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