A159349 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,0} transformation (see link).
1, 1, 1, 4, 11, 24, 56, 129, 300, 698, 1623, 3773, 8771, 20390, 47401, 110194, 256170, 595523, 1384423, 3218393, 7481856, 17393205, 40434296, 93998334, 218519615, 507996473, 1180948523, 2745372238, 6382216141, 14836852470, 34491497366
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
- Richard Choulet, Curtz-like transformation.
- Index entries for linear recurrences with constant coefficients, signature (3,-2,1).
Programs
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Magma
I:=[56, 129, 300]; [1,1,1,4,11,24] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): n in [1..50]]; // G. C. Greubel, Jun 16 2018
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Maple
a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=56:a(7):=129:a(8):=300:for n from 6 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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Mathematica
Join[{1, 1, 1, 4, 11, 24}, LinearRecurrence[{3, -2, 1}, {56, 129, 300}, 95]] (* G. C. Greubel, Jun 16 2018 *) -
PARI
m=50; v=concat([56,129,300], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1,1,1,4,11,24], v) \\ G. C. Greubel, Jun 16 2018
Formula
O.g.f.: (1-2x+2x^3-2x^5+2x^6-2x^7+x^8)/(1-3x+2x^2-x^3). [corrected by Georg Fischer, May 19 2019]
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>=9, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11, a(5)=24, a(6)=56, a(7)=129, a(8)=300.