A121428 Rectangular table, read by antidiagonals, where row n is equal to column 2 of matrix power A121412^(n+1) for n>=0.

1, 1, 1, 1, 2, 5, 1, 3, 11, 45, 1, 4, 18, 101, 581, 1, 5, 26, 169, 1305, 9730, 1, 6, 35, 250, 2190, 21745, 199692, 1, 7, 45, 345, 3255, 36360, 443329, 4843125, 1, 8, 56, 455, 4520, 53916, 737051, 10679494, 135345925, 1, 9, 68, 581, 6006, 74781, 1087583, 17645187

Offset

0,5

Links

Table of n, a(n) for n=0..52.

Example

Table of column 2 in matrix powers of triangle H=A121412 begins:
H^1: 1, 1, 5, 45, 581, 9730, 199692, 4843125, 135345925, ...
H^2: 1, 2, 11, 101, 1305, 21745, 443329, 10679494, 296547736, ...
H^3: 1, 3, 18, 169, 2190, 36360, 737051, 17645187, 487025244, ...
H^4: 1, 4, 26, 250, 3255, 53916, 1087583, 25889969, 710546530, ...
H^5: 1, 5, 35, 345, 4520, 74781, 1502270, 35578270, 971255050, ...
H^6: 1, 6, 45, 455, 6006, 99351, 1989113, 46890210, 1273698270, ...
H^7: 1, 7, 56, 581, 7735, 128051, 2556806, 60022670, 1622857887, ...
H^8: 1, 8, 68, 724, 9730, 161336, 3214774, 75190410, 2024181693, ...
H^9: 1, 9, 81, 885, 12015, 199692, 3973212, 92627235, 2483617140, ...
Rearrangement of the upper part of the table forms A121432, which is
the number of subpartitions of partition [0,0,0,1,1,1,1,2,2,2,2,2,..]:
1,1,1, 1,2,3,4, 5,11,18,26,35, 45,101,169,250,345,455, 581,1305,...

Prog

(PARI) {T(n, k)=local(H=Mat(1), B); for(m=1, k+3, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(H^i)[i-1, j]); )); H=B); return((H^(n+1))[k+3, 3])}

Crossrefs

Cf. A121429 (diagonal), A121431; rows: A121414, A121419, A121423; related tables: A121424, A121426; related triangles: A121412, A121416, A121420.

Sequence in context: A100084 A269598 A100226 * A239969 A105686 A316131

Adjacent sequences: A121425 A121426 A121427 * A121429 A121430 A121431

Keyword

nonn,tabl

Author

Paul D. Hanna, Aug 26 2006

Status

approved