A094195 Expansion of g.f.: (1-4*x)/((1-5*x)*(1-x)^2).

1, 3, 10, 42, 199, 981, 4888, 24420, 122077, 610359, 3051766, 15258798, 76293955, 381469737, 1907348644, 9536743176, 47683715833, 238418579115, 1192092895522, 5960464477554, 29802322387711, 149011611938493, 745058059692400, 3725290298461932, 18626451492309589

Offset: 0

Author

N. J. A. Sloane, Jun 01 2004

Keywords

• nonn
• easy

Comments

An approximation to A091843.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
• F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
• Index entries for sequences related to Gijswijt's sequence
• Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Crossrefs

Cf. A047926, A073724, A090822, A091843.

A row of A094250.

Programs

Magma

[(5^(n+1) +12*n +11)/16: n in [0..40]]; // G. C. Greubel, Aug 18 2023

Mathematica

CoefficientList[Series[(1-4x)/((1-5x)(1-x)^2),{x,0,30}],x] (* or *) LinearRecurrence[{7,-11,5},{1,3,10},30] (* Harvey P. Dale, Dec 31 2011 *)

SageMath

[(5^(n+1) +12*n +11)/16 for n in range(41)] # G. C. Greubel, Aug 18 2023

Formula

a(n) = (5^(n+1) + 12*n + 11)/16.

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3), with a(0)=1, a(1)=3, a(2)=10. - Harvey P. Dale, Dec 31 2011

E.g.f.: (1/16)*(5*exp(5*x) + (11 + 12*x)*exp(x)). - G. C. Greubel, Aug 18 2023