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