A110666 Sequence is {a(1,n)}, where a(m,n) is defined at sequence A110665.

0, 1, 1, -2, -6, -6, 0, 7, 7, -2, -12, -12, 0, 13, 13, -2, -18, -18, 0, 19, 19, -2, -24, -24, 0, 25, 25, -2, -30, -30, 0, 31, 31, -2, -36, -36, 0, 37, 37, -2, -42, -42, 0, 43, 43, -2, -48, -48, 0, 49, 49, -2, -54, -54, 0, 55, 55, -2, -60, -60, 0, 61, 61, -2, -66, -66, 0, 67, 67, -2, -72, -72, 0, 73, 73, -2, -78, -78, 0, 79, 79, -2, -84

Offset

0,4

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Formula

From R. J. Mathar, Oct 09 2013: (Start)

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

a(n) = -A010892(n-1) + A165202(n) -1. (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, ...

Maple

A11066x := proc(mmax, nmax) local a, i, j ; a := array(0..mmax, 0..nmax) ; a[0, 0] := 0 ; for i from 1 to nmax do a[0, i] := i-sum(binomial(2*i-k-1, i-1)*a[0, k], k=0..i-1) : od ; for j from 1 to mmax do a[j, 0] := 0 ; for i from 1 to nmax do a[j, i] := a[j-1, i]+a[j, i-1] ; od ; od ; RETURN(a) ; end : nmax := 100 : m := 1: a := A11066x(m, nmax) : for n from 0 to nmax do printf("%d, ", a[m, n]) ; od ; # R. J. Mathar, Sep 01 2006

Mathematica

a[m_, 0] := 0; a[n_, n_] := n; a[0, n_] := n - Sum[Binomial[2*n - k - 1, n - 1]* a[0, k], {k, 0, n - 1}]; a[m_, n_] := a[m, n] = a[m - 1, n] + a[m, n - 1]; Table[a[1, n], {n, 0, 50}] (* G. C. Greubel, Sep 03 2017 *)

Crossrefs

Cf. A110665, A110667, A110668, A110669, A110670, A110671, A110672.

Sequence in context: A019716 A106152 A197036 * A200485 A201318 A242001

Adjacent sequences: A110663 A110664 A110665 * A110667 A110668 A110669

Keyword

easy,sign

Author

Leroy Quet, Aug 02 2005

Extensions

More terms from R. J. Mathar, Sep 01 2006

Status

approved