The On-Line Encyclopedia of Integer Sequences (OEIS)

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A193662

Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)
(history; published version)

#7 by R. J. Mathar at Thu Feb 19 14:23:51 EST 2015

STATUS

editing

approved

#6 by R. J. Mathar at Thu Feb 19 14:23:21 EST 2015

FORMULA

Conjecture: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) if n>3. - R. J. Mathar, Feb 19 2015

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:57:38 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Aug 02 2011

Discussion

Fri Mar 30

18:57

OEIS Server: https://oeis.org/edit/global/285

#4 by T. D. Noe at Tue Aug 02 15:46:08 EDT 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Tue Aug 02 15:37:00 EDT 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Tue Aug 02 15:06:11 EDT 2011

NAME

allocated Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for Clark Kimberling0<=i<=j. (See Comments.)

DATA

2, 1, 5, 7, 25, 51, 149, 351, 945, 2347, 6125, 15511, 40009, 102051, 262085, 670287, 1718625, 4399771, 11274269, 28873351

OFFSET

0,1

COMMENTS

For the definition of Q-residue, see A193649.

MATHEMATICA

q[n_, k_] := 1;

r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];

f[n_, x_] := LucasL[n, x]; (* A114525 *)

p[n_, k_] := Coefficient[f[n, x], x, k];

v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

Table[v[n], {n, 0, 16}] (* A193662 *)

TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

Table[r[k], {k, 0, 8}]

TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, 4}]]

CROSSREFS

Cf. A193649, A114525.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Aug 02 2011

STATUS

approved

editing

#1 by Clark Kimberling at Tue Aug 02 09:27:03 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved