A008825 Expansion of (1+2*x^5+x^9)/((1-x)^2*(1-x^9)).

1, 2, 3, 4, 5, 8, 11, 14, 17, 22, 27, 32, 37, 42, 49, 56, 63, 70, 79, 88, 97, 106, 115, 126, 137, 148, 159, 172, 185, 198, 211, 224, 239, 254, 269, 284, 301, 318, 335, 352, 369, 388, 407, 426, 445, 466, 487, 508, 529, 550, 573, 596, 619, 642, 667, 692, 717

Offset

0,2

Links

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

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

Formula

a(n) = floor((2*n^2 + 3*n + 9)/9) + ((n-3) mod 9) - ((n-1) mod 9) + 2)/9. - G. C. Greubel, Sep 13 2019

a(n) = 1 + floor(n*(2*n + 3)/9) + [mod(n-1,9)<2], where [] is the Iverson bracket. - Michel Marcus, Sep 14 2019

Example

G.f. = 1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 11*x^6 + 14*x^7 + 17*x^8 + ...

Maple

seq(coeff(series((1+2*x^5+x^9)/((1-x)^2*(1-x^9)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Sep 13 2019

Mathematica

CoefficientList[Series[(1+2*x^5+x^9)/((1-x)^2*(1-x^9)), {x, 0, 50}], x] (* G. C. Greubel, Sep 13 2019 *)

Prog

(PARI) a(n)=floor((2*n^2+3*n)/9)+1+((n-1)%9<2) \\ Tani Akinari, Jun 01 2014
(PARI) {a(n) = ((n + 1) * (2*n + 1) + 4*(2 + (n%9%4>0))) \ 9}; /* Michael Somos, Jun 01 2014 */
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+2*x^5+x^9)/((1-x)^2*(1-x^9)) )); // G. C. Greubel, Sep 13 2019
(Sage)
def A008825_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+2*x^5+x^9)/((1-x)^2*(1-x^9))).list()
A008825_list(50) # G. C. Greubel, Sep 13 2019
(GAP) a:=[1, 2, 3, 4, 5, 8, 11, 14, 17, 22, 27];; for n in [12..50] do a[n]:= 2*a[n-1]-a[n-2] +a[n-9]-2*a[n-10]+a[n-11]; od; a; # G. C. Greubel, Sep 13 2019

Crossrefs

Expansions of the form (1 +2*x^(m+1) +x^(2*m+1))/((1-x)^2*(1-x^(2*m+1))): A008822 (m=1), A008823 (m=2), A008824 (m=3), this sequence (m=4).

Sequence in context: A144679 A309679 A207890 * A261629 A244395 A271488

Adjacent sequences: A008822 A008823 A008824 * A008826 A008827 A008828

Keyword

nonn

Author

N. J. A. Sloane

Status

approved