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A111522 Sequence is {a(4,n)}, where a(m,n) is defined at sequence A111518. 5
1, 4, 7, 4, -4, -5, -49, -200, 59, 10, -5240, 11936, 30806, -412987, 1352862, 3166014, -57455111, 263800403, 200944299, -11339467789, 77531515035, -118123511262, -2692592328869, 29677554626711, -125561516944238, -528175322368741, 13093479718202187 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

EXAMPLE

a(0,n): 1,0,-3,-4,7,...

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

a(2,n): 1,2,0,-6,-5,...

a(3,n): 1,3,3,-3,-8,...

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

Main diagonal is 1,1,0,-3,-4,..., which is 1 followed by sequence a(0,n).

MAPLE

A111522T := proc(nmax) local a, m, n; a := array(0..nmax, 0..nmax) ; for m from 0 to nmax do a[m, 0] := 1 ; od ; for n from 1 to nmax do a[n, n] := a[0, n-1] ; for m from n+1 to nmax do a[m, n] := a[m-1, n]+a[m, n-1] ; od ; for m from n-1 to 0 by -1 do a[m, n] := a[m+1, n]-a[m+1, n-1] ; od ; od ; RETURN(a) ; end: nmax := 50 ; a := A111522T(nmax) ; m := 4 ; for n from 0 to nmax do printf("%d, ", a[m, n]) ; od; # R. J. Mathar, Sep 26 2006

MATHEMATICA

nmax = 26;

a[_, 0] = 1;

a[m_ /; m > 0, n_ /; n > 0] := a[m, n] = a[m - 1, n] + a[m, n - 1];

sol = Solve[Table[a[n + 1, n + 1] == a[0, n], {n, 0, nmax}], Table[a[0, n], {n, 1, nmax + 1}], Integers] // First;

Do[a[m, n] = a[m, n] /. sol, {m, 0, nmax}, {n, 0, nmax}];

Table[a[4, n], {n, 0, nmax}] (* Jean-Fran├žois Alcover, Sep 21 2020 *)

CROSSREFS

Cf. A111518, A111519, A111520, A111521, A111523.

Sequence in context: A019626 A203137 A005472 * A342203 A019735 A202501

Adjacent sequences:  A111519 A111520 A111521 * A111523 A111524 A111525

KEYWORD

easy,sign

AUTHOR

Leroy Quet, Aug 05 2005

EXTENSIONS

More terms from R. J. Mathar, Sep 26 2006

STATUS

approved

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)