A026762
a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.
Original entry on oeis.org
1, 4, 16, 66, 279, 1201, 5242, 23133, 103015, 462269, 2088146, 9487405, 43328580, 198798447, 915950385, 4236322720, 19661850045, 91549502656, 427539667095, 2002120576312, 9399659155395, 44234927105888, 208631813215116
Offset: 1
Cf.
A026747,
A026758,
A026759,
A026760,
A026761,
A026763,
A026764,
A026765,
A026766,
A026767,
A026768.
-
T:= proc(n,k) option remember;
if n<0 then 0;
elif k=0 or k = n then 1;
elif type(n,'odd') and 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) ;
end if ;
end proc;
seq(T(2*n-1,n-1), n=1..30); # G. C. Greubel, Oct 31 2019
-
T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && 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] ]]]; Table[T[2n-1, n-1], {n, 0, 30}] (* G. C. Greubel, Oct 31 2019 *)
-
@CachedFunction
def T(n, k):
if (n<0): return 0
elif (k==0 or k==n): return 1
elif (mod(n,2)==1 and 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(2*n-1, n-1) for n in (1..30)] # G. C. Greubel, Oct 31 2019
Original entry on oeis.org
1, 15, 141, 1070, 7187, 44673, 263431, 1496218, 8266100, 44718596, 238015318, 1250656153, 6504202391, 33543967700, 171810543570, 875006817465, 4435130657170, 22390449598704, 112654298838120, 565172299571352
Offset: 4
Original entry on oeis.org
1, 12, 95, 629, 3781, 21433, 116928, 621317, 3239925, 16662600, 84804868, 428176176, 2148404051, 10726889402, 53349600116, 264499086453, 1308025259637, 6455291067020, 31804649415803, 156486128169860, 769098411417361
Offset: 3
Original entry on oeis.org
1, 5, 22, 95, 411, 1790, 7855, 34725, 154573, 692450, 3120206, 14135555, 64356345, 294341325, 1351889910, 6233399525, 28845511125, 133933280000, 623811120960, 2913924782375, 13648296620445, 64087737455725, 301644762913977
Offset: 1
-
a(n)=if(n<1,0,subst(polinterpolate(Vec((1-3*x-sqrt(1-6*x+5*x^2+x^2*O(x^n)))/2)),x,n+1))
Original entry on oeis.org
1, 7, 37, 178, 823, 3737, 16833, 75608, 339610, 1527944, 6892210, 31186533, 141598200, 645186895, 2950261555, 13538266219, 62338173865, 287993085103, 1334712682675, 6204513729392, 28925212243136, 135216169757852, 633722949713612
Offset: 2
Original entry on oeis.org
1, 9, 56, 301, 1504, 7217, 33821, 156274, 716116, 3266558, 14868789, 67649170, 307997855, 1404343584, 6416130302, 29383457373, 134915391509, 621163581667, 2867888163907, 13278007815855, 61645847283931, 286977785803129
Offset: 3
Original entry on oeis.org
1, 11, 79, 472, 2554, 13024, 63958, 306382, 1443463, 6725059, 31101315, 143160979, 657181579, 3012930550, 13810302898, 63339713546, 290848317898, 1337717758649, 6164619409085, 28469921477415, 131784947615381, 611477036684719
Offset: 4
A026866
a(n) = T(2n+1,n+2), T given by A026747.
Original entry on oeis.org
1, 6, 29, 132, 589, 2613, 11592, 51558, 230181, 1032060, 4648150, 21027765, 95542878, 435939525, 1997076805, 9183661080, 42383777344, 196271453865, 911804206063, 4248637465050, 19852810349837, 93012949698861, 436860932671829
Offset: 1
Original entry on oeis.org
1, 8, 46, 234, 1124, 5241, 24050, 109429, 495884, 2244060, 10158768, 46055322, 209247370, 953184750, 4354605139, 19954396521, 91721631238, 422908476612, 1955876264342, 9072401893299, 42203220058991, 196862017041783, 920700735516741
Offset: 2
Original entry on oeis.org
1, 10, 67, 380, 1976, 9771, 46845, 220232, 1022498, 4710021, 21593848, 98750485, 451158834, 2061525163, 9429060852, 43193760271, 198255105055, 912011899565, 4205605922556, 19442627224940, 90115768761346, 418762733418510
Offset: 3
Comments