0,2

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.

Column k of R^2 = column 1 of P^(2k+1) for k>=0 where triangle P = A135880; column 0 of R^2 = column 1 of P; column 1 of R^2 = column 1 of P^3; column 2 of R^2 = column 1 of P^5.

Triangle R^2 begins:

1;

2, 1;

7, 6, 1;

34, 39, 10, 1;

215, 300, 95, 14, 1;

1698, 2741, 990, 175, 18, 1;

16220, 29380, 11635, 2296, 279, 22, 1;

182714, 363922, 154450, 32865, 4410, 407, 26, 1;

2378780, 5135894, 2302142, 517916, 74319, 7524, 559, 30, 1;

35219202, 81557270, 38229214, 8980944, 1353522, 145805, 11830, 735, 34, 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; ...

where column k of R = column 0 of P^(2k+1)

and 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; ...

where column k of P equals column 0 of R^(k+1).

(PARI) {T(n, k)=local(P=Mat(1), R=Mat(1), 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]))))); (R^2)[n+1, k+1]}

Cf. A135882 (column 0), A135890 (column 1); A135894 (R), A135880 (P), A135888 (P^3), A135892 (P^5).

Sequence in context: A077230 A019668 A091700 this_sequence A039814 A078301 A060583

Adjacent sequences: A135892 A135893 A135894 this_sequence A135896 A135897 A135898

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 15 2007