A026902
a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), m=[ (n+1)/2 ], T given by A026780.
Original entry on oeis.org
1, 1, 4, 5, 18, 24, 84, 115, 400, 554, 1934, 2690, 9474, 13180, 46962, 65193, 235338, 325568, 1191292, 1641192, 6086880, 8348342, 31369180, 42831204, 162943236, 221515918, 852512496, 1154208486, 4489722568, 6055426942
Offset: 1
A027246
a(n) = greatest number in row n of array T given by A026780.
Original entry on oeis.org
1, 1, 3, 5, 12, 24, 53, 117, 246, 580, 1178, 2916, 6150, 14834, 32656, 76221, 173719, 395048, 926664, 2063104, 4958556, 10847078, 26619438, 59372770, 143365880, 326086492, 774562478, 1792293014, 4197344582, 9861375614
Offset: 0
A027247
a(n) = self-convolution of row n of array T given by A026780.
Original entry on oeis.org
1, 2, 11, 42, 216, 926, 4805, 21594, 113176, 523158, 2766030, 13043426, 69508528, 332880898, 1786840975, 8666578226, 46835595908, 229627064562, 1248785459646, 6180314464290, 33808696703208, 168713818115262, 927994263768204, 4665292098508258, 25791693351775736
Offset: 0
A027248
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026780.
Original entry on oeis.org
1, 6, 29, 156, 741, 3958, 19233, 103340, 513829, 2782642, 14111035, 76987001, 396866211, 2179190558, 11387537287, 62869497136, 332264796115, 1842788400972, 9831563838105, 54737178645869, 294362713929617, 1644215891925732, 8902034364734719, 49863044050919951
Offset: 1
A027249
a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026780.
Original entry on oeis.org
1, 9, 59, 338, 1937, 10289, 57345, 299832, 1663421, 8705069, 48391863, 254818488, 1421911953, 7544528179, 42264280735, 225949128338, 1270219491983, 6838142459779, 38557301241769, 208865221891584, 1180647902778713, 6430734346787925, 36426544777112515, 199364753897943071
Offset: 2
A027250
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026780.
Original entry on oeis.org
1, 12, 95, 639, 3917, 23377, 132553, 762434, 4201955, 23901906, 130453555, 740755012, 4035754137, 22952934073, 125259143235, 714206660342, 3909459844469, 22346990842402, 122748276118411, 703146926077588, 3875572768594421, 22238537172443007, 122969745150601115
Offset: 3
A027251
a(n) = Sum_{k=0..n} (k+1) * A026780(n, k).
Original entry on oeis.org
1, 3, 10, 27, 76, 195, 519, 1299, 3364, 8311, 21191, 51981, 131273, 320715, 804845, 1961823, 4901782, 11932489, 29719325, 72291325, 179610365, 436699813, 1082870377, 2632116551, 6516122403, 15835522783, 39147779575
Offset: 0
A027252
a(n) = Sum_{k=0..n} (k+1) * A026780(n, n-k).
Original entry on oeis.org
1, 3, 10, 28, 80, 211, 569, 1455, 3806, 9564, 24565, 61080, 155041, 382920, 964163, 2370712, 5934974, 14548685, 36266755, 88711181, 220415107, 538305745, 1334040167, 3254193849, 8047710361, 19613210297, 48419611161
Offset: 0
A027253
Sum of squares of numbers in row n of array T given by A026780.
Original entry on oeis.org
1, 2, 11, 43, 220, 984, 5110, 24200, 127649, 626505, 3345863, 16847161, 90863911, 466507567, 2536185547, 13221761945, 72350925134, 381847149426, 2100852968144, 11199635371558, 61899477831260, 332745848952712, 1846197664841460, 9994041629456490, 55635847260490940
Offset: 0
A026769
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(2,1)=2; for n >= 3 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1<=k<=(n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 7, 4, 1, 1, 8, 17, 11, 5, 1, 1, 10, 31, 28, 16, 6, 1, 1, 12, 49, 76, 44, 22, 7, 1, 1, 14, 71, 156, 120, 66, 29, 8, 1, 1, 16, 97, 276, 352, 186, 95, 37, 9, 1, 1, 18, 127, 444, 784, 538, 281, 132, 46, 10, 1, 1, 20, 161, 668, 1504, 1674, 819, 413, 178, 56, 11, 1
Offset: 0
Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 6, 7, 4, 1;
1, 8, 17, 11, 5, 1;
1, 10, 31, 28, 16, 6, 1;
1, 12, 49, 76, 44, 22, 7, 1;
1, 14, 71, 156, 120, 66, 29, 8, 1;
1, 16, 97, 276, 352, 186, 95, 37, 9, 1;
1, 18, 127, 444, 784, 538, 281, 132, 46, 10, 1;
-
T:= function(n,k)
if k=0 or k=n then return 1;
elif (n=2 and k=1) then return 2;
elif (k <= Int((n-1)/2)) then return T(n-1,k-1)+T(n-2,k-1) +T(n-1,k);
else return T(n-1,k-1) + T(n-1,k);
fi;
end;
Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # G. C. Greubel, Oct 31 2019
-
A026769 := proc(n,k)
option remember;
if k= 0 or k =n then
1;
elif n= 2 and k= 1 then
2;
elif k <= (n-1)/2 then
procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
else
procname(n-1,k-1)+procname(n-1,k) ;
fi ;
end proc: # R. J. Mathar, Jun 15 2014
-
T[n_, k_] := T[n, k] = Which[k==0 || k==n, 1, n==2 && k==1, 2, k <= (n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], True, T[n-1, k-1] + T[n-1, k]];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 10 2017, from Maple *)
-
T(n,k) = if(k==0 || k==n, 1, if(n==2 && k==1, 2, if( k<=(n-1)/2, T(n-1,k-1) + T(n-2,k-1) + T(n-1,k), T(n-1,k-1) + T(n-1,k) )));
for(n=0,12, for(k=0,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Oct 31 2019
-
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
elif (n==2 and k==1): return 2
elif (k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
else: return T(n-1,k-1) + T(n-1,k)
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Oct 31 2019
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