A237716 7-distance Pell sequence.

1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 13, 15, 23, 25, 37, 39, 55, 65, 85, 111, 135, 185, 213, 295, 343, 465, 565, 735, 935, 1161, 1525, 1847, 2455, 2977, 3925, 4847, 6247, 7897, 9941, 12807, 15895, 20657, 25589, 33151, 41383, 53033, 66997

Offset

0,8

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,2).

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1; a(n) = 2*a(n-7) + a(n-2) for n>=7.

G.f.: (1 + x)/(1 - x^2 - 2*x^7).

a(2*n) = Sum_{j=0..n/7} binomial(n-5*j, 2*j)*2^(2*j) + Sum_{j=0..(n-4)/7} binomial(n-3-5*j, 2*j+1)*2^(2*j+1).

a(2*n+1) = Sum_{j=0..n/7} binomial(n-5*j, 2*j)*2^(2*j) + Sum_{j=0..(n-3)/7} binomial(n-2-5*j, 2*j+1)*2^(2*j+1).

Example

a(7)=2a(0)+a(5)=3; a(8)=2a(1)+a(6)=3; a(9)=2a(2)+a(7)=5.

Mathematica

For[j = 0, j < 7, j++, a[j] = 1]
For[j = 7, j < 51, j++, a[j] = 2 a[j - 7] + a[j - 2]]
Table[a[j], {j, 0, 50}]
CoefficientList[Series[(1 + x)/(1 - x^2 - 2 x^7), {x, 0, 50}], x] (* G. C. Greubel, May 01 2017 *)

Prog

(PARI) Vec((1+x)/(1-x^2-2*x^7)+O(x^99)) \\ Charles R Greathouse IV, Mar 06 2014

Crossrefs

Cf. A000129, A122522, A159284, A237714.

Sequence in context: A245148 A339104 A073737 * A245147 A339103 A187072

Adjacent sequences: A237713 A237714 A237715 * A237717 A237718 A237719

Keyword

nonn,easy

Author

Sergio Falcon, Feb 12 2014

Status

approved