A037754 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 2,3,1,0.

2, 17, 120, 840, 5882, 41177, 288240, 2017680, 14123762, 98866337, 692064360, 4844450520, 33911153642, 237378075497, 1661646528480, 11631525699360, 81420679895522, 569944759268657, 3989613314880600, 27927293204164200

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (8,-8,8,-7).

Formula

a(n) = (1/2)*floor(7^(n+1)/10). - Mircea Merca, Dec 27 2010

a(n) = +8*a(n-1) -8*a(n-2) +8*a(n-3) -7*a(n-4) for n > 4. - R. J. Mathar, Jan 03 2011

a(n) = -1/4 +7^(n+1)/20 -(-1)^floor(n/2)*A000034(n)/10. - R. J. Mathar, Jan 03 2011

G.f.: x*(2+x) / ( (x-1)*(7*x-1)*(x^2+1) ). - R. J. Mathar, Jan 03 2011

Maple

seq(1/2*floor(7^n/10), n=2..22); # Mircea Merca, Dec 27 2010

Mathematica

Table[FromDigits[PadRight[{}, n, {2, 3, 1, 0}], 7], {n, 20}] (* or *) LinearRecurrence[ {8, -8, 8, -7}, {2, 17, 120, 840}, 20] (* Harvey P. Dale, Sep 23 2021 *)

Prog

(Magma) Periodic2310:=func< n | &cat[ [ [2, 3, 1, 0][1+(k mod 4)]: k in [0..n-1] ] ] >; /* initial segment of length n */
[ Seqint(Reverse(Periodic2310(n)), 7): n in [1..25] ];

Crossrefs

Related sequences based on different periods of length 4 are A037761, A037677, A037684, A037691, A037698, A037705, A037712, A037719, A037726, A037733, A037740, A037747, A037768, A037775, A037782, A037789, A037796.

Sequence in context: A198043 A037747 A037628 * A037642 A161128 A220403

Adjacent sequences: A037751 A037752 A037753 * A037755 A037756 A037757

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved