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A027011 Triangular array T read by rows: T(n,k) = t(n, 2k+1) for 0 <= k <= floor((2n-1)/2), t given by A027960, n >= 0. 18
3, 3, 4, 3, 7, 5, 3, 7, 15, 6, 3, 7, 18, 28, 7, 3, 7, 18, 44, 47, 8, 3, 7, 18, 47, 98, 73, 9, 3, 7, 18, 47, 120, 199, 107, 10, 3, 7, 18, 47, 123, 291, 373, 150, 11, 3, 7, 18, 47, 123, 319, 661, 654, 203, 12, 3, 7, 18, 47, 123, 322, 806, 1404, 1085, 267, 13, 3, 7, 18, 47 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Right-edge columns are polynomials approximating Lucas(2n).
LINKS
FORMULA
T(n, k) = Lucas(2n) = A005248(n) for 2k+1 <= n, otherwise the (2n-2k+1)-th coefficient of the power series for (1+2x)/((1-x-x^2)(1-x)^(2k-n+1)).
EXAMPLE
3
3, 4
3, 7, 5
3, 7, 15, 6
3, 7, 18, 28, 7
3, 7, 18, 44, 47, 8
3, 7, 18, 47, 98, 73, 9
3, 7, 18, 47, 120, 199, 107, 10
3, 7, 18, 47, 123, 291, 373, 150, 11
MAPLE
t:=proc(n, k)option remember:if(k=0 or k=2*n)then return 1:elif(k=1)then return 3:else return t(n-1, k-2) + t(n-1, k-1):fi:end:
T:=proc(n, k)return t(n, 2*k+1):end:
for n from 0 to 8 do for k from 0 to floor((2*n-1)/2) do print(T(n, k)); od:od: # Nathaniel Johnston, Apr 18 2011
MATHEMATICA
t[n_, k_] := t[n, k] = If[k == 0 || k == 2*n, 1, If[k == 1, 3, t[n-1, k-2] + t[n-1, k-1]]]; T[n_, k_] := t[n, 2*k+1]; Table[T[n, k], {n, 1, 12}, {k, 0, (2*n-1)/2}] // Flatten (* Jean-François Alcover, Nov 18 2013, after Nathaniel Johnston *)
CROSSREFS
This is a bisection of the "Lucas array " A027960, see A026998 for the other bisection.
Right-edge columns include A027965, A027967, A027969, A027971.
An earlier version of this entry had (unjustifiably) each row starting with 1.
Sequence in context: A342137 A062069 A163375 * A339400 A267048 A350502
KEYWORD
nonn,easy,tabl
AUTHOR
EXTENSIONS
Edited by Ralf Stephan, May 05 2005
STATUS
approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)