A110576
Sequence is {a(0,n)}, where a(m,0)=1, a(m,n) = a(m,n-1) + a(m-1,n), a(0,n+1) = a(n,n).
Original entry on oeis.org
1, 1, 2, 7, 29, 132, 648, 3407, 19109, 113946, 719896, 4802318, 33712717, 248285282, 1912928549, 15379305080, 128729241725, 1119519156562, 10097102345993, 94285391374568, 910145431036423, 9069616636456648, 93179779321299479
Offset: 0
a(0,n): 1, 1, 2, 7, 29
a(1,n): 1, 2, 4, 11
a(2,n): 1, 3, 7, 18
a(3,n): 1, 4, 11, 29
Since a(3,3) = 29, a(0,4) also is 29.
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a[0, 0] := 1; a[0, 1] := 1; a[0, n_] := a[0, n] = Sum[Binomial[2*n - k - 3, n - 2]*a[0, k], {k, 0, n - 1}]; Table[a[0,n], {n,0,50}] (* G. C. Greubel, Aug 31 2017 *)
A110577
{a(1,n)}, where a(m,n) is defined in sequence A110576.
Original entry on oeis.org
1, 2, 4, 11, 40, 172, 820, 4227, 23336, 137282, 857178, 5659496, 39372213, 287657495, 2200586044, 17579891124, 146309132849, 1265828289411, 11362930635404
Offset: 0
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a[0, 0] := 1; a[0, 1] := 1; a[0, n_] := a[0, n] = Sum[Binomial[2*n - k - 3, n - 2]*a[0, k], {k, 0, n - 1}]; a[1, 0] := 1; a[1, n_] := a[1, n] = a[1, n - 1] + a[0, n]; Table[a[1, n], {n, 0, 50}] (* G. C. Greubel, Aug 31 2017 *)
A110578
{a(2,n)}, where a(m,n) is as defined in sequence A110576.
Original entry on oeis.org
1, 3, 7, 18, 58, 230, 1050, 5277, 28613, 165895, 1023073, 6682569, 46054782, 333712277, 2534298321, 20114189445, 166423322294, 1432251611705, 12795182247109, 118443504257081, 1134237257303476, 11219647646806519
Offset: 0
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a[0, 0] := 1; a[0, 1] := 1; a[0, n_] := a[0, n] = Sum[Binomial[2*n - k - 3, n - 2]*a[0, k], {k, 0, n - 1}]; a[1, 0] := 1; a[1, n_] := a[1, n] = a[1, n - 1] + a[0, n]; a[2, 0] := 1; a[2, n_] := a[2, n] = a[2, n - 1] + a[1, n]; Table[a[2, n], {n, 0, 50}] (* G. C. Greubel, Sep 01 2017 *)
A110579
{a(3,n)}, where a(m,n) is as defined in sequence A110576.
Original entry on oeis.org
1, 4, 11, 29, 87, 317, 1367, 6644, 35257, 201152, 1224225, 7906794, 53961576, 387673853, 2921972174, 23036161619, 189459483913, 1621711095618, 14416893342727, 132860397599808, 1267097654903284
Offset: 0
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a[0, 0] := 1; a[0, 1] := 1; a[0, n_] := a[0, n] = Sum[Binomial[2*n - k - 3, n - 2]*a[0, k], {k, 0, n - 1}]; a[1, 0] := 1; a[1, n_] := a[1, n] = a[1, n - 1] + a[0, n]; a[2, 0] := 1; a[2, n_] := a[2, n] = a[2, n - 1] + a[1, n]; a[3, 0] := 1; a[3, n_] := a[3, n] = a[3, n - 1] + a[2, n];
Table[a[3, n], {n, 0, 50}] (* G. C. Greubel, Sep 01 2017 *)
Showing 1-4 of 4 results.
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