A100477
a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3) if n>=3, otherwise a(n) = n.
Original entry on oeis.org
0, 1, 2, 8, 29, 105, 381, 1382, 5013, 18184, 65960, 239261, 867887, 3148143, 11419464, 41422565, 150254766, 545028892, 1977018773, 7171368869, 26013173045, 94359275646, 342275541897, 1241558350028, 4503585409524
Offset: 0
gamo (gamo(AT)telecable.es), Nov 22 2004
-
[n le 3 select n-1 else 3*Self(n-1)+2*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, May 20 2015
-
RecurrenceTable[{a[n]== 3a[n-1] +2a[n-2] +a[n-3], a[0]==0, a[1]==1, a[2]==2}, a, {n,0,26}] (* or *)
CoefficientList[ Series[(x^2-x)/(x^3+2x^2+3x-1), {x,0,26}], x] (* Robert G. Wilson v, May 19 2015 *)
LinearRecurrence[{3,2,1},{0,1,2},40] (* Harvey P. Dale, Jun 19 2015 *)
-
#!/usr/local/bin/perl -w $d=0; $c=1; $b=2; print "$d,$c,$b,"; $a=0; for (;;){ $a=3*$b+2*$c+$d; $d=$c; $c=$b; $b=$a; print "$a,"; last if ($a >2**61); } _END_
-
@CachedFunction
def a(n): # a = A100477
if (n<3): return n
else: return 3*a(n-1)+2*a(n-2)+a(n-3)
[a(n) for n in range(41)] # G. C. Greubel, Apr 06 2023
A010911
Pisot sequence E(3,11), a(n) = floor(a(n-1)^2/a(n-2) + 1/2).
Original entry on oeis.org
3, 11, 40, 145, 526, 1908, 6921, 25105, 91065, 330326, 1198213, 4346356, 15765820, 57188385, 207443151, 752472043, 2729490816, 9900859685, 35914032730, 130273308376, 472548850273, 1714107200301, 6217692609825, 22553841080350, 81811015661001, 296758421753528
Offset: 0
- Colin Barker, Table of n, a(n) for n = 0..1000
- D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.
- D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
- S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016).
- Index entries for linear recurrences with constant coefficients, signature (3,2,1).
-
LinearRecurrence[{3, 2, 1}, {3, 11, 40}, 30] (* Jean-François Alcover, Oct 05 2018 *)
-
x='x+O('x^33); Vec((3+2*x+x^2)/(1-3*x-2*x^2-x^3)) \\ Altug Alkan, Oct 05 2018
A108136
a(1)=1; a(2)=1; a(3)=1; a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3).
Original entry on oeis.org
1, 1, 1, 6, 21, 76, 276, 1001, 3631, 13171, 47776, 173301, 628626, 2280256, 8271321, 30003101, 108832201, 394774126, 1431989881, 5194350096, 18841804176, 68346102601, 247916266251, 899282808131, 3262027059496, 11832563061001
Offset: 1
-
LinearRecurrence[{3, 2, 1}, {1, 1, 1}, 30]
A108152
a(n)= 3*a(n-1) +2*a(n-2) +a(n-3).
Original entry on oeis.org
1, 0, 2, 7, 25, 91, 330, 1197, 4342, 15750, 57131, 207235, 751717, 2726752, 9890925, 35877996, 130142590, 472074687, 1712387237, 6211453675, 22531210186, 81728925145, 296460649482, 1075371008922, 3900763250875, 14149492419951
Offset: 0
-
M = {{0, 1, 0}, {0, 0, 1}, {1, 2, 3}} a3 = Table[MatrixPower[M, i][[1, 2]], {i, 1, 50}]
LinearRecurrence[{3,2,1},{1,0,2},30] (* Harvey P. Dale, Jun 06 2016 *)
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
Showing 1-4 of 4 results.
Comments