|
Search: id:A097712
|
|
|
| A097712 |
|
Lower triangular matrix T, read by rows, such that T(n,0) = 1 and T(n,k) = T(n-1,k) + T^2(n-1,k-1) for k>0, where T^2 is the matrix square of T. |
|
+0
9
|
|
| 1, 1, 1, 1, 3, 1, 1, 8, 7, 1, 1, 25, 44, 15, 1, 1, 111, 346, 208, 31, 1, 1, 809, 4045, 3720, 912, 63, 1, 1, 10360, 77351, 99776, 35136, 3840, 127, 1, 1, 236952, 2535715, 4341249, 2032888, 308976, 15808, 255, 1, 1, 9708797, 145895764, 319822055, 189724354
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums form A016121. Column 1 forms A097713. This triangle has the same row sums and first column terms as in rows 2^n, for n>=0, of triangle A093662.
|
|
EXAMPLE
|
T(5,1) = T(4,1) + T^2(4,0) = 25 + 86 = 111.
T(5,2) = T(4,2) + T^2(4,1) = 44 + 302 = 346.
T(5,3) = T(4,3) + T^2(4,2) = 15 + 193 = 208.
Rows of T begin:
[1],
[1,1],
[1,3,1],
[1,8,7,1],
[1,25,44,15,1],
[1,111,346,208,31,1],
[1,809,4045,3720,912,63,1],
[1,10360,77351,99776,35136,3840,127,1],
[1,236952,2535715,4341249,2032888,308976,15808,255,1],
[1,9708797,145895764,319822055,189724354,37329584,2608864,64256,511,1],...
Rows of T^2 begin:
[1],
[2,1],
[5,6,1],
[17,37,14,1],
[86,302,193,30,1],
[698,3699,3512,881,62,1],
[9551,73306,96056,34224,3777,126,1],
[226592,2458364,4241473,1997752,305136,15681,254,1],
[9471845,143360049,315480806,187691466,37020608,2593056,64001,510,1],...
Column 0 of T^2 forms A016121.
Row sums of T^2 form the first differences of A016121.
|
|
PROGRAM
|
(PARI) {T(n, k)=if(n<0|k>n, 0, if(n==k, 1, if(k==0, 1, T(n-1, k)+sum(j=0, n-1, T(n-1, j)*T(j, k-1)); )))}
|
|
CROSSREFS
|
Cf. A016121, A093662, A097713, A097710.
Adjacent sequences: A097709 A097710 A097711 this_sequence A097713 A097714 A097715
Sequence in context: A134380 A124469 A094816 this_sequence A034801 A102435 A100537
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Aug 24 2004
|
|
|
Search completed in 0.002 seconds
|
