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A226392 Triangle with first column identical to 1 and the other entries defined by the sum of entries above and to the left. 2
1, 1, 1, 1, 2, 3, 1, 4, 8, 13, 1, 8, 20, 42, 71, 1, 16, 48, 120, 256, 441, 1, 32, 112, 320, 792, 1698, 2955, 1, 64, 256, 816, 2256, 5532, 11880, 20805, 1, 128, 576, 2016, 6096, 16488, 40140, 86250, 151695, 1, 256, 1280, 4864, 15872, 46432, 123680 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The sequence of row sums s(n) starts at n=0 as 1, 2, 6, 26, 142, 882, 5910, 41610, 303390,... and appears to obey the hypergeometric recurrence n*s(n) +2*(7-5*n)*s(n-1) +9*(n-2)*s(n-2)=0.

LINKS

Table of n, a(n) for n=0..51.

FORMULA

Definition: T(n,0)=1. T(n,k) = sum_{0<=c<k} T(n,c) + sum_{k<=r<n} T(r,k) for k>0.

T(n,3) = 6*T(n-1,3) -12*T(n-2,3)+8*T(n-3,3). T(n,3) = 2^n*(n+10)*(n-1)/16.

T(n,4) = 8*T(n-1,4) -24*T(n-2,4) +32*T(n-3,4) -16*T(n-4,4); T(n,4) = 2^n*(n^2/4 +65*n/96 -47/16 +n^3/96).

EXAMPLE

T(3,2) = 8 = 3 (above) +1+4 (to the left).

1;

1,1;

1,2,3;

1,4,8,13;

1,8,20,42,71;

1,16,48,120,256,441;

1,32,112,320,792,1698,2955;

1,64,256,816,2256,5532,11880,20805;

MAPLE

A226392 := proc(n, k)

    option remember;

    if k = 0 then

        1;

    elif k > n or k < 0 then

        0 ;

    else

        add( procname(n, c), c=0..k-1) + add( procname(r, k), r=k..n-1) ;

    end if;

end proc:

MATHEMATICA

t[_, 0] = 1; t[n_, k_] := t[n, k] = Sum[t[n, c], {c, 0, k-1}] + Sum[t[r, k], {r, k, n-1}]; Table[t[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Jan 10 2014 *)

CROSSREFS

Cf. A162326 (diagonal), A000079 (column k=1), A001792 (column k=2).

Sequence in context: A321629 A075297 A057597 * A121340 A231206 A165241

Adjacent sequences:  A226389 A226390 A226391 * A226393 A226394 A226395

KEYWORD

nonn,tabl,easy

AUTHOR

R. J. Mathar, Jun 06 2013

STATUS

approved

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)