0,4

G.f. of n-th upper diagonal: D(x,n) = D(x,0)*G(x)^n where G(x) = 1 + x*G(x)^4 ; i.e., the g.f. of the n-th upper diagonal, D(x,n), equals the product of the g.f. of the main diagonal, D(x,0) and the n-th power of G(x) where G(x) is the g.f. of A002293.

Square array begins:

(1), 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...;

(1), (2), 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...;

(3), 7, (12), 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, ...;

(7), 25, 50, (83), 125, 177, 240, 315, 403, 505, 622, 755, 905, ...;

(25), 75, 200, 377, (617), 932, 1335, 1840, 2462, 3217, 4122, 5195, ...;

(75), 275, 652, 1584, 2919, (4759), 7221, 10438, 14560, 19755, 26210,..;

(275), 927, 2511, 5430, 12651, 23089, (37649), 57404, 83614, 117746,...;

(927), 3438, 8868, 21519, 44608, 102012, 185626, (303372), 464867, ...;

(3438), 12306, 33825, 78433, 180445, 366071, 830938, 1512611, (2480181), ...; ...

For each row, removing terms enclosed in parenthesis and then taking partial sums yields the next row.

(PARI) {T(n, k)=if(k<0, 0, if(n==0, 1, T(n, k-1) + if(n-1>k+1, T(n-1, k+1), T(n-1, k+2))))}

Cf. A130463 (first column), A130464 (main diagonal); A002293.

Sequence in context: A094531 A161009 A111960 this_sequence A059380 A145035 A122832

Adjacent sequences: A130459 A130460 A130461 this_sequence A130463 A130464 A130465

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), May 26 2007