A130462 Square array, read by antidiagonals, where row n+1 equals the partial sums of the sequence resulting from removing the terms in the first column and main diagonal from row n, for n>=0, with row 0 consisting of all 1's.

1, 1, 1, 3, 2, 1, 7, 7, 3, 1, 25, 25, 12, 4, 1, 75, 75, 50, 18, 5, 1, 275, 275, 200, 83, 25, 6, 1, 927, 927, 652, 377, 125, 33, 7, 1, 3438, 3438, 2511, 1584, 617, 177, 42, 8, 1, 12306, 12306, 8868, 5430, 2919, 932, 240, 52, 9, 1, 46131, 46131, 33825, 21519, 12651, 4759

Offset

0,4

Comments

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.

Links

Table of n, a(n) for n=0..60.

Example

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.

Prog

(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))))}

Crossrefs

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

Sequence in context: A274293 A161009 A111960 * A059380 A145035 A359413

Adjacent sequences: A130459 A130460 A130461 * A130463 A130464 A130465

Keyword

nonn,tabl

Author

Paul D. Hanna, May 26 2007

Status

approved