A262964 Lower triangular matrix. See comments for definition.

1, 1, 0, 1, 0, 1, 1, 0, 3, 0, 1, 0, 6, 1, 2, 1, 0, 10, 4, 9, 0, 1, 0, 15, 10, 28, 7, 5, 1, 0, 21, 20, 69, 36, 30, 1

Offset

1,9

Comments

Handmade table created by looking at the "columns" that are separated by zeros in the Mathematica program output. First column is A000012. Second column A000004. Third column A000217. Fourth column A000292. At least a few columns onwards are recognized by the OEIS automated sequence recognition as polynomials.

Row sums are A239605. Alternating row sums are A011782.

Links

Table of n, a(n) for n=1..36.

Example

Triangle starts and row sums are A239605:
   1                                    =    1
   1    0                               =    1
   1    0    1                          =    2
   1    0    3    0                     =    4
   1    0    6    1    2                =   10
   1    0   10    4    9    0           =   24
   1    0   15   10   28    7    5      =   66
   1    0   21   20   69   36   30    1 =  178
Alternating row sums are A011782:
   1                                    =    1
   1   -0                               =    1
   1   -0    1                          =    2
   1   -0    3   -0                     =    4
   1   -0    6   -1    2                =    8
   1   -0   10   -4    9   -0           =   16
   1   -0   15  -10   28   -7    5      =   32
   1   -0   21  -20   69  -36   30   -1 =   64

Mathematica

(* To get this number triangle, look at the numbers separated by zeros in the columns *)
(* coefficients (coeff) in power series can be changed *)Clear[t, n, k, i, nn, x];
Clear[x]
coeff = {1, 1000000000000000000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
mp[m_, e_] :=
If[e == 0, IdentityMatrix@Length@m, MatrixPower[m, e]]; nn =
Length[coeff]; cc = Range[nn]*0 + 1; Monitor[
Do[Clear[t]; t[n_, 1] := t[n, 1] = cc[[n]];
  t[n_, k_] :=
   t[n, k] =
    If[n >= k,
     Sum[t[n - i, k - 1], {i, 1, k - 1}] -
      Sum[t[n - i, k], {i, 1, k - 1}], 0];
  A4 = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
  A5 = A4[[1 ;; nn - 1]]; A5 = Prepend[A5, ConstantArray[0, nn]];
  cc = Total[
    Table[coeff[[n]]*mp[A5, n - 1][[All, 1]], {n, 1, nn}]]; , {i, 1,
   nn}], i];
cc;
TableForm[A4[[All, 1]]]

Crossrefs

Cf. Row sums A239605, alternating row sums A011782, columns: A000012, A000004, A000217, A000292.

Sequence in context: A238341 A242451 A363978 * A135481 A180049 A244454

Adjacent sequences: A262961 A262962 A262963 * A262965 A262966 A262967

Keyword

tabl,nonn

Author

Mats Granvik, Oct 05 2015

Status

approved