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A110665 Sequence is {a(0,n)}, where a(m,0)=0, a(m,n) = a(m-1,n)+a(m,n-1) and a(0,n) is such that a(n,n) = n for all n. 9
0, 1, 0, -3, -4, 0, 6, 7, 0, -9, -10, 0, 12, 13, 0, -15, -16, 0, 18, 19, 0, -21, -22, 0, 24, 25, 0, -27, -28, 0, 30, 31, 0, -33, -34, 0, 36, 37, 0, -39, -40, 0, 42, 43, 0, -45, -46, 0, 48, 49, 0, -51, -52, 0, 54, 55, 0, -57, -58, 0, 60, 61, 0, -63, -64, 0, 66, 67, 0, -69, -70, 0, 72, 73, 0, -75, -76, 0, 78, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-3,2,-1).

FORMULA

a(0, n) = n - Sum_{k=0..(n-1)} binomial(2*n-k-1, n-1)*a(0, k).

From Franklin T. Adams-Watters, May 12 2006: (Start)

a(n) = n * A010892(n), where A010892 is periodic sequence [1,1,0,-1,-1,0].

G.f.: (x-2*x^2)/(1-x+x^2)^2. (End)

EXAMPLE

a(0,n): 0, 1, 0, -3, -4,...

a(1,n): 0, 1, 1, -2, -6,...

a(2,n): 0, 1, 2, 0, -6,...

a(3,n): 0, 1, 3, 3, -3,...

a(4,n): 0, 1, 4, 7, 4,...

Main diagonal of array is 0, 1, 2, 3, 4,...

MATHEMATICA

LinearRecurrence[{2, -3, 2, -1}, {0, 1, 0, -3}, 80] (* Harvey P. Dale, Dec 19 2015 *)

a[0, n_] := a[0, n] = If[n < 3, {0, 1, 0}[[n+1]], (n((n-2)a[0, n-1] - (n-1)a[0, n-2]))/((n-1)(n-2))];

Table[a[0, n], {n, 0, 79}] (* Jean-Fran├žois Alcover, Mar 29 2020 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec((x-2*x^2)/(1-x+x^2)^2)) \\ G. C. Greubel, Sep 03 2017 *)

CROSSREFS

Cf. A110666 - A110672.

Sequence in context: A337164 A105576 A105826 * A063441 A319600 A092894

Adjacent sequences:  A110662 A110663 A110664 * A110666 A110667 A110668

KEYWORD

easy,sign

AUTHOR

Leroy Quet, Aug 02 2005

EXTENSIONS

More terms from Franklin T. Adams-Watters, May 12 2006

STATUS

approved

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Last modified April 20 09:13 EDT 2021. Contains 343125 sequences. (Running on oeis4.)