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A135896 Triangle, read by rows, equal to R^3, the matrix cube of R = A135894. 2
1, 3, 1, 15, 9, 1, 99, 81, 15, 1, 814, 816, 195, 21, 1, 8057, 9366, 2625, 357, 27, 1, 93627, 122148, 38270, 6006, 567, 33, 1, 1252752, 1795481, 611525, 105910, 11439, 825, 39, 1, 19003467, 29478724, 10721093, 1996988, 236430, 19404, 1131, 45, 1, 322722064 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

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

EXAMPLE

Triangle R^3 begins:

1;

3, 1;

15, 9, 1;

99, 81, 15, 1;

814, 816, 195, 21, 1;

8057, 9366, 2625, 357, 27, 1;

93627, 122148, 38270, 6006, 567, 33, 1;

1252752, 1795481, 611525, 105910, 11439, 825, 39, 1;

19003467, 29478724, 10721093, 1996988, 236430, 19404, 1131, 45, 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).

PROG

(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^3)[n+1, k+1]}

CROSSREFS

Cf. A135883 (column 0); A135894 (R), A135880 (P), A135888 (P^3), A135892 (P^5).

Sequence in context: A113389 A038553 A282629 * A134144 A035342 A039815

Adjacent sequences:  A135893 A135894 A135895 * A135897 A135898 A135899

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 15 2007

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)