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1, 1, 3, 9, 23, 59, 153, 401, 1063, 2847, 7693, 20947, 57413, 158265, 438467, 1220145, 3408759, 9556815, 26878861, 75815839, 214411865, 607827693, 1726911631, 4916352891, 14022750725, 40066540277, 114666463855, 328662240617
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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Conjecture: D-finite with recurrence n*a(n) +(-7*n+4)*a(n-1) +(13*n-10)*a(n-2) +(n-34)*a(n-3) +(-13*n+84)*a(n-4) +(3*n-32)*a(n-5) +(-n+6)*a(n-6) +3*(n-6)*a(n-7)=0. - R. J. Mathar, Jun 15 2020
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MAPLE
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T:= proc(n, k) option remember;
if k<0 or k>2*n then 0
elif k=0 or k=2 or k=2*n then 1
elif k=1 then 0
else add(T(n-1, k-j), j=1..3)
fi
end:
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[T[n, 2*n-2], {n, 30}] (* G. C. Greubel, Nov 06 2019 *)
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PROG
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(Sage)
@CachedFunction
def T(n, k):
if (k<0 or k>2*n): return 0
elif (k==0 or k==2 or k==2*n): return 1
elif (k==1): return 0
else: return sum(T(n-1, k-j) for j in (1..3))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Offset changed to 1 and a(1)=1 prepended to sequence by G. C. Greubel, Nov 06 2019
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STATUS
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approved
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