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A163313 Triangle read by rows, A010766 convolved with A014668 (diagonalized as an infinite lower triangular matrix) 3
1, 2, 1, 3, 1, 3, 4, 2, 3, 7, 5, 2, 3, 7, 16, 6, 3, 6, 7, 16, 33, 7, 3, 6, 7, 16, 33, 71, 8, 4, 6, 14, 16, 33, 71, 143, 9, 4, 9, 14, 16, 33, 71, 143, 295, 10, 5, 9, 14, 32, 33, 71, 143, 295, 594 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is an eigentriangle (i.e., a lower triangular matrix * a diagonalized version of its eigensequence); A014668 is the eigensequence of triangle A010766.

Row sums = A014668 starting (1, 3, 7, 16, 33, 71, 143, ...).

Sum of n-th row terms = rightmost term of next row.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

Equals M * Q as infinite lower triangular matrices, where M = triangle A010766 and Q = a matrix with A014668: (1, 1, 3, 7, 16, 33, 71, 143, ...) as the main diagonal and the rest zeros.

EXAMPLE

First few rows of the triangle =

   1;

   2,  1;

   3,  1,  3;

   4,  2,  3,  7;

   5,  2,  3,  7, 16;

   6,  3,  6,  7, 16, 33;

   7,  3,  6,  7, 16, 33  71;

   8,  4,  6, 14, 16, 33, 71, 143;

   9,  4,  9, 14, 16, 33, 71, 143, 295;

  10,  5,  9, 14, 32, 33, 71, 143, 295, 594;

  11,  5,  9, 14, 32, 33, 71, 143, 295, 594, 1206;

  12,  6, 12, 21, 32, 66, 71, 143, 295, 594, 1206, 2413;

  ...

Example: row 4 = (4, 2, 3, 7) = (4, 2, 1, 1) * (1, 1, 3, 7).

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Sum[Sum[a[d], {d, Divisors[k]}], {k, 1, n -1}];

Table[Floor[n/k]* a[k], {n, 1, 5}, {k, 1, n}]//Flatten (* G. C. Greubel, Dec 18 2016 *)

CROSSREFS

Cf. A010766, A014668.

Sequence in context: A143802 A177040 A336887 * A337178 A321893 A308673

Adjacent sequences:  A163310 A163311 A163312 * A163314 A163315 A163316

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson & Mats Granvik, Jul 30 2009

STATUS

approved

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Last modified June 23 01:56 EDT 2021. Contains 345394 sequences. (Running on oeis4.)