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A237718 9-distance Pell numbers. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 15, 17, 25, 27, 39, 41, 57, 59, 79, 89, 113, 139, 167, 217, 249, 331, 367, 489, 545, 715, 823, 1049, 1257, 1547, 1919, 2281, 2897, 3371, 4327, 5017, 6425, 7531, 9519 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

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

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

FORMULA

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=1, a(8)=1; a(n) = 2*a(n-9) + a(n-2) for n>=9.

G.f. (1+x)/(1-x^2-2x^9).

a(2*n) = Sum_{j=0..n/9} Binomial[n-7j, 2j]*2^{2j} + Sum_{j=0..(n-5)/9} Binomial[n-4-7j, 2j+1]*2^{2j+1}.

a(2*n+1) = Sum_{j=0..n/9} Binomial[n-7j, 2j]*2^{2j} + Sum_{j=0..(n-4)/9} Binomial[n-3-7j, 2j+1]*2^{2j+1}.

EXAMPLE

a(9)=2a(0)+a(7)=3; a(10)=2a(1)+a(8)=3; a(11)=2a(2)+a(9)=5.

MATHEMATICA

For[j = 0, j < 9, j++, a[j] = 1]

For[j = 9, j < 51, j++, a[j] = 2 a[j - 9] + a[j - 2]]

Table[a[j], {j, 0, 50}]

CoefficientList[Series[(1 + x)/(1 - x^2 - 2 x^9), {x, 0, 50}], x] (* G. C. Greubel, May 01 2017 *)

PROG

(PARI) Vec((1+x)/(1-x^2-2*x^9)+O(x^99)) \\ Charles R Greathouse IV, Mar 06 2014

CROSSREFS

Cf. A000129, A122522, A159284, A237714, A237716, A237717.

Sequence in context: A339110 A245150 A339109 * A245149 A339108 A206914

Adjacent sequences:  A237715 A237716 A237717 * A237719 A237720 A237721

KEYWORD

nonn,easy

AUTHOR

Sergio Falcon, Feb 12 2014

STATUS

approved

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Last modified October 2 13:05 EDT 2022. Contains 357205 sequences. (Running on oeis4.)