A290986 Expansion of x^6/((1 - x)^2*(1 - 2*x + x^3 - x^4)).

1, 4, 11, 25, 52, 103, 199, 379, 716, 1346, 2523, 4721, 8825, 16487, 30791, 57494, 107343, 200400, 374116, 698403, 1303770, 2433846, 4543428, 8481513, 15832975, 29556394, 55174730, 102998026, 192272662, 358927018, 670030771

Offset: 6

Author

R. J. Mathar, Aug 16 2017

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 6..3688
• T. Langley, J. Liese, and J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order, J. Int. Seq. 14 (2011) # 11.4.2.
• Index entries for linear recurrences with constant coefficients, signature (4,-5,1,3,-3,1).

Crossrefs

Cf. A049858, A290987, A290989.

Programs

Magma

I:=[1,4,11,25,52,103]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2)+Self(n-3)+3*Self(n-4)-3*Self(n-5)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Aug 17 2017

Maple

f:= gfun:-rectoproc({a(n)-a(n+1)+2*a(n+3)-a(n+4)+n-1, a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 0, a(4) = 0, a(5) = 0, a(6) = 1}, a(n), remember):
map(f, [$6..100]); # Robert Israel, Aug 17 2017

Mathematica

 LinearRecurrence[{4,-5,1,3,-3,1}, {1,4,11,25,52,103}, 40] (* Vincenzo Librandi, Aug 17 2017 *)

PARI

Vec(x^6/((1-x)^2*(1-2*x+x^3-x^4)) + O(x^50)) \\ Michel Marcus, Aug 17 2017

SageMath

def A290986_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x^6/((1-x)^2*(1-2*x+x^3-x^4)) ).list()
a=A290986_list(50); a[6:] # G. C. Greubel, Apr 12 2023

Formula

a(n) = A049858(n-2) - (n-2).