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A233522 Expansion of 1 / (1 - x - x^4 + x^9) in powers of x. 3
1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 29, 38, 50, 67, 89, 118, 156, 207, 274, 363, 481, 638, 845, 1119, 1482, 1964, 2602, 3447, 4566, 6049, 8013, 10615, 14062, 18629, 24678, 32691, 43306, 57369, 75998, 100676, 133367, 176674, 234043, 310041, 410717 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

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

FORMULA

a(n) = a(n-1) + a(n-4) - a(n-9) for all n in Z.

a(n) - a(n-1) = A017830(n).

G.f.: 1 / ((1 - x) * (1 + x) * (1 + x^2) * (1 - x - x^5)).

EXAMPLE

G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ If[ n >= 0, 1 / (1 - x - x^4 + x^9), -x^9 / (1 - x^5 - x^8 + x^9)], {x, 0, Abs@n}];

PROG

(PARI) {a(n) = if( n>=0, polcoeff( 1 / (1 - x - x^4 + x^9) + x * O(x^n), n), polcoeff( -x^9 / (1 - x^5 - x^8 + x^9) + x * O(x^-n), -n))};

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/( 1-x-x^4+x^9))); // G. C. Greubel, Aug 08 2018

CROSSREFS

Cf. A017830.

Sequence in context: A120149 A117597 A241336 * A112639 A290137 A336351

Adjacent sequences:  A233519 A233520 A233521 * A233523 A233524 A233525

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Dec 11 2013

STATUS

approved

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)