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A262964
Lower triangular matrix. See comments for definition.
1
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.
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
KEYWORD
tabl,nonn
AUTHOR
Mats Granvik, Oct 05 2015
STATUS
approved