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 A159349 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,0} transformation (see link). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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). 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. 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); MATHEMATICA Join[{1, 1, 1, 4, 11, 24}, LinearRecurrence[{3, -2, 1}, {56, 129, 300}, 95]] (* G. C. Greubel, Jun 16 2018 *) PROG (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 (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 CROSSREFS Cf. A137531, A159347, A159348. Sequence in context: A007678 A159350 A159348 * A192597 A181946 A176959 Adjacent sequences:  A159346 A159347 A159348 * A159350 A159351 A159352 KEYWORD easy,nonn AUTHOR Richard Choulet, Apr 11 2009 STATUS approved

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)