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A128590 Triangle read by rows, matrix product A128179 * A000012. 0
1, 2, 2, 4, 3, 3, 6, 6, 4, 4, 9, 8, 8, 5, 5, 12, 12, 10, 6, 6, 16, 15, 15, 12, 12, 7, 7, 20, 20, 18, 18, 14, 14, 8, 8, 25, 24, 24, 21, 21, 16, 16, 9, 9, 30, 30, 28, 28, 24, 24, 18, 18, 10, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = the tetrahedral numbers, A000292, starting (1, 4, 10, 20, 35, 56, 84, ...).

LINKS

Table of n, a(n) for n=1..54.

FORMULA

A128179 * A000012 as infinite lower triangular matrices.

Regarded as an array by antidiagonals A(i, j) = degree in q of q-Fibonacci number F(i+2, j-1) where F(1, k) = F(2, k) = 1, F(n, k) = F(n-1, k) + q^(n+k-2) * F(n-2, k). - Michael Somos, Jun 08 2011

EXAMPLE

First few rows of the triangle are:

1;

2, 2;

4, 3, 3;

6, 6, 4, 4;

9, 8, 8, 5, 5;

12, 12, 10, 6, 6;

16, 15, 15, 12, 12, 7, 7;

...

First few rows of the array are:

1,  2,  3,  4,  5,  6,  7,  8, ...

2,  3,  4,  5,  6,  7,  8,  9, ...

4,  6,  8, 10, 12, 14, 16, 18, ...

6,  8, 10, 12, 14, 16, 18, 20, ...

9, 12, 15, 18, 21, 24, 27, 30, ...

...

A(3, 4) = 10 because F(5, 3) = 1 + q^4 + q^5 + q^6 + q^10. A(4, 4) = 12 because F(6, 3) = 1 + q^4 + q^5 + q^6 + q^7 + q^10 + q^11 + q^12.

PROG

(PARI) {T(n, k) = (n - k + 2)\2 * ((n + k + 1)\2)} /* Michael Somos, Jun 08 2011 */

CROSSREFS

Cf. A128179, A000012, A000292.

Sequence in context: A147594 A212652 A205678 * A143228 A143211 A209755

Adjacent sequences:  A128587 A128588 A128589 * A128591 A128592 A128593

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Mar 11 2007

STATUS

approved

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Last modified September 25 16:16 EDT 2017. Contains 292499 sequences.