A193771 Expansion of 1 / (1 - x - x^3 + x^6) in powers of x.

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

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