A092076 Expansion of (1+4*x^3+x^6)/((1-x)*(1-x^3)^2).

1, 1, 1, 7, 7, 7, 19, 19, 19, 37, 37, 37, 61, 61, 61, 91, 91, 91, 127, 127, 127, 169, 169, 169, 217, 217, 217, 271, 271, 271, 331, 331, 331, 397, 397, 397, 469, 469, 469, 547, 547, 547, 631, 631, 631, 721, 721, 721, 817, 817, 817, 919, 919, 919, 1027, 1027, 1027, 1141, 1141

Offset: 0

Author

N. J. A. Sloane, Mar 29 2004

Keywords

• nonn
• easy

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A003215.

Programs

Magma

I:=[1,1,1,7,7,7,19]; [n le 7 select I[n] else Self(n-1)+2*Self(n-3)-2*Self(n-4)-Self(n-6)+Self(n-7): n in [1..70]]; // Vincenzo Librandi, Jul 13 2015

Maple

f:= gfun:-rectoproc({q(n+3)-3*q(n+2)+3*q(n+1)-q(n), q(0) = 1, q(1) = 7, q(2) = 19},q(n),remember):
seq(f(i)$3, i=0..30); # Robert Israel, Jul 14 2015

Mathematica

CoefficientList[Series[(1 + 4*x^3 + x^6)/((1 - x)*(1 - x^3)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 23 2015 *)
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 1, 1, 7, 7, 7, 19}, 60] (* Vincenzo Librandi, Jul 13 2015 *)
With[{c=LinearRecurrence[{3,-3,1},{1,7,19},20]},{c,c,c}]//Flatten//Sort (* Harvey P. Dale, Aug 03 2019 *)

Formula

G.f.: (1+4*x^3+x^6)/((1-x)*(1-x^3)^2).

a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7), n>7. - Wesley Ivan Hurt, Jun 23 2015

A003215 with each term repeated three times: a(n) = A003215(floor(n/3)). - Robert Israel, Jul 14 2015