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A105535 Triangular matrix T, read by rows, where diagonal n equals T^(n+1) when flattened (as read by rows), for n>=0. 4
1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 4, 2, 1, 5, 1, 9, 4, 1, 1, 6, 1, 16, 6, 1, 1, 1, 7, 1, 25, 8, 1, 6, 3, 1, 8, 1, 36, 10, 1, 17, 8, 1, 1, 9, 1, 49, 12, 1, 36, 15, 2, 1, 1, 10, 1, 64, 14, 1, 65, 24, 3, 1, 1, 1, 11, 1, 81, 16, 1, 106, 35, 4, 1, 12, 4, 1, 12, 1, 100, 18, 1, 161, 48, 5, 1, 61, 26 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The ratio of consecutive row sums seems to converge to a value near 2, but it is not yet certain that the limit exists.

LINKS

Table of n, a(n) for n=0..89.

EXAMPLE

Triangle begins:

1;

1,1;

1,2,1;

1,3,1,1;

1,4,1,4,2;

1,5,1,9,4,1;

1,6,1,16,6,1,1;

1,7,1,25,8,1,6,3;

1,8,1,36,10,1,17,8,1;

1,9,1,49,12,1,36,15,2,1;

1,10,1,64,14,1,65,24,3,1,1; ...

which when flattened (read by rows) forms diagonal 0:

1,1,1,1,2,1,1,3,1,1,1,4,1,4,2,1,5,1,9,4,1,...

The matrix square, T^2 = A105537, begins:

1;

2,1;

4,4,1;

6,8,2,1;

12,26,7,12,4; ...

which when flattened (read by rows) forms diagonal 1:

1,2,1,4,4,1,6,8,2,1,12,26,7,12,4,...

The matrix cube, T^3 = A105539, begins:

1;

3,1;

9,6,1;

17,15,3,1;

61,92,23,28,8; ...

which when flattened (read by rows) forms diagonal 2:

1,3,1,9,6,1,17,15,3,1,61,92,23,28,8,...

PROG

(PARI) {T(n, k)=local(A=matrix(n+1, n+1, r, c, if(r>=c, 1)), B, TK=floor((sqrt(8*k+1)-1)/2), TC); B=A; for(r=0, n, for(c=0, r, TC=floor((sqrt(8*c+1)-1)/2); B[r+1, c+1]=(A^(r-c+1))[TC+1, c-TC*(TC+1)/2+1]); A=B); return((A^(n-k+1))[TK+1, k-TK*(TK+1)/2+1])}

CROSSREFS

Cf. A105536 (row sums), A105537 (matrix square), A105539 (matrix cube).

Sequence in context: A165430 A164823 A167269 * A182980 A244051 A207974

Adjacent sequences:  A105532 A105533 A105534 * A105536 A105537 A105538

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Apr 12 2005

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)