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A193771 Expansion of  1 / (1 - x - x^3 + x^6) in powers of x. 1
1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 17, 23, 31, 41, 54, 72, 96, 127, 168, 223, 296, 392, 519, 688, 912, 1208, 1600, 2120, 2809, 3721, 4929, 6530, 8651, 11460, 15181, 20111, 26642, 35293, 46753, 61935, 82047, 108689, 143982, 190736, 252672, 334719, 443408, 587391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

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

FORMULA

G.f.: 1 / (1 - x - x^3 + x^6) = 1 / (1 - x / (1 - x^2 / (1 + x^2 / (1 - x / (1 + x / (1 + x^2 / (1 - x^2))))))).

a(n) = a(n-1) + a(n-3) - a(n-6) for all n in Z.

Convolution of A008621 and A000931. PSUM transform of A017818.

EXAMPLE

G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 7*x^7 + 10*x^8 + 13*x^9 + ...

MATHEMATICA

CoefficientList[Series[1/(1-x-x^3+x^6), {x, 0, 50}], x] (* or *) LinearRecurrence[ {1, 0, 1, 0, 0, -1}, {1, 1, 1, 2, 3, 4}, 50] (* Harvey P. Dale, Jul 25 2017 *)

PROG

(PARI) {a(n) = if( n<0, n = -n; polcoeff( - x^6 / (1 - x^3 - x^5 + x^6) + x * O(x^n), n), polcoeff( 1 / (1 - x - x^3 + x^6) + x * O(x^n), n))};

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^3+x^6)));  // G. C. Greubel, Aug 10 2018

CROSSREFS

Cf. A000931, A008621, A017818.

Sequence in context: A106507 A006950 A052335 * A160333 A174578 A241733

Adjacent sequences:  A193768 A193769 A193770 * A193772 A193773 A193774

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 01 2013

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)