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A136225
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Matrix square of triangle A136220, read by rows.
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8
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1, 2, 1, 8, 4, 1, 49, 26, 6, 1, 414, 232, 54, 8, 1, 4529, 2657, 629, 92, 10, 1, 61369, 37405, 9003, 1320, 140, 12, 1, 996815, 627435, 153276, 22606, 2385, 198, 14, 1, 18931547, 12248365, 3031553, 450066, 47500, 3904, 266, 16, 1, 412345688, 273211787
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 of this triangle = column 1 of square array A136217.
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FORMULA
| Let P=A136220, V=A136230, then column k of P^2 (this triangle) = column 0 of V^(k+1) while column j of V = column 0 of P^(3j+2).
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EXAMPLE
| Let P = A136220, then this triangle is P^2 and begins:
1;
2, 1;
8, 4, 1;
49, 26, 6, 1;
414, 232, 54, 8, 1;
4529, 2657, 629, 92, 10, 1;
61369, 37405, 9003, 1320, 140, 12, 1;
996815, 627435, 153276, 22606, 2385, 198, 14, 1;
18931547, 12248365, 3031553, 450066, 47500, 3904, 266, 16, 1; ...
where column k of P^2 = column 0 of V^(k+1) and
triangle V = A136230 begins:
1;
2, 1;
8, 5, 1;
49, 35, 8, 1;
414, 325, 80, 11, 1;
4529, 3820, 988, 143, 14, 1;
61369, 54800, 14696, 2200, 224, 17, 1; ...
where column k of V = column 0 of P^(3k+2).
Triangle P = A136220 begins:
1;
1, 1;
3, 2, 1;
15, 10, 3, 1;
108, 75, 21, 4, 1;
1036, 753, 208, 36, 5, 1;
12569, 9534, 2637, 442, 55, 6, 1;
185704, 146353, 40731, 6742, 805, 78, 7, 1; ...
where column k of P = column 0 of U^(k+1) and U = A136228.
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PROG
| (PARI) {T(n, k)=local(P=Mat(1), U, PShR); if(n>0, for(i=0, n, PShR=matrix(#P, #P, r, c, if(r>=c, if(r==c, 1, if(c==1, 0, P[r-1, c-1])))); U=P*PShR^2; U=matrix(#P+1, #P+1, r, c, if(r>=c, if(r<#P+1, U[r, c], if(c==1, (P^3)[ #P, 1], (P^(3*c-1))[r-c+1, 1])))); P=matrix(#U, #U, r, c, if(r>=c, if(r<#R, P[r, c], (U^c)[r-c+1, 1]))))); (P^2)[n+1, k+1]}
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CROSSREFS
| Cf. columns: A136226, A136227; related tables: A136228 (U), A136230 (V), A136231 (W=P^3), A136217, A136218.
Sequence in context: A109979 A110171 A104988 * A089460 A178102 A135520
Adjacent sequences: A136222 A136223 A136224 * A136226 A136227 A136228
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 28 2008
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