A135892 Triangle, read by rows, equal to P^5, where triangle P = A135880.

1, 5, 1, 30, 10, 1, 220, 95, 15, 1, 1945, 990, 195, 20, 1, 20340, 11635, 2625, 330, 25, 1, 247066, 154450, 38270, 5440, 500, 30, 1, 3430936, 2302142, 611525, 94515, 9750, 705, 35, 1, 53741404, 38229214, 10721093, 1761940, 196500, 15870, 945, 40, 1

Offset: 0

Author

Paul D. Hanna, Dec 15 2007

Keywords

• nonn
• tabl

Comments

Triangle P = A135880 is defined by: column k of P^2 equals column 0 of P^(2k+2) such that column 0 of P^2 equals column 0 of P shift left.

Examples

			Triangle P^5 begins:
1;
5, 1;
30, 10, 1;
220, 95, 15, 1;
1945, 990, 195, 20, 1;
20340, 11635, 2625, 330, 25, 1;
247066, 154450, 38270, 5440, 500, 30, 1;
3430936, 2302142, 611525, 94515, 9750, 705, 35, 1;
53741404, 38229214, 10721093, 1761940, 196500, 15870, 945, 40, 1;
938816814, 701685738, 205607124, 35429974, 4182295, 363820, 24115, 1220, 45, 1;
where P = A135880 begins:
1;
1, 1;
2, 2, 1;
6, 7, 3, 1;
25, 34, 15, 4, 1;
138, 215, 99, 26, 5, 1;
970, 1698, 814, 216, 40, 6, 1; ...
in which column k of P = column 0 of R^(k+1),
where R = A135894 begins:
1;
1, 1;
2, 3, 1;
6, 12, 5, 1;
25, 63, 30, 7, 1;
138, 421, 220, 56, 9, 1;
970, 3472, 1945, 525, 90, 11, 1; ...
in which column k of R equals column 0 of P^(2k+1).
		

Crossrefs

Cf. A135880 (P), A135894 (R), A135895 (R^2), A135896 (R^3), A135897 (R^4).

Programs

PARI

{T(n,k)=local(P=Mat(1),R,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]))));R=P*PShR; R=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,R[r,c], if(c==1,(P^2)[ #P,1],(P^(2*c-1))[r-c+1,1])))); P=matrix(#R, #R, r,c, if(r>=c, if(r<#R,P[r,c], (R^c)[r-c+1,1])))));(P^5)[n+1,k+1]}

Formula

Column k of P^5 = column 2 of R^(k+1) for k>=0 where triangle R = A135894; column 0 of P^5 = column 2 of R; column 1 of P^5 = column 2 of R^2; column 2 of P^5 = column 2 of R^3; column 3 of P^5 = column 2 of R^4.