A371754
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).
Original entry on oeis.org
1, 3, 15, 85, 505, 3081, 19125, 120173, 761995, 4865697, 31244029, 201544551, 1305039209, 8477521051, 55221311565, 360559717807, 2359123470971, 15463951609491, 101530816122729, 667587477393509, 4395294402200983, 28972295880583861, 191181607835416543
Offset: 0
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Table[Sum[Binomial[3n-2k,n-3k],{k,0,Floor[n/3]}],{n,0,30}] (* Harvey P. Dale, Oct 19 2024 *)
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a(n) = sum(k=0, n\3, binomial(3*n-2*k, n-3*k));
A371743
a(n) = Sum_{k=0..floor(n/2)} binomial(4*n-k,n-2*k).
Original entry on oeis.org
1, 4, 29, 231, 1926, 16491, 143683, 1267395, 11282393, 101151544, 912011633, 8260998772, 75115815749, 685232639419, 6268299350776, 57478389714473, 528167137069958, 4862304525663579, 44836026545219765, 414048025058547788, 3828677665694353049
Offset: 0
A371744
a(n) = Sum_{k=0..floor(n/2)} binomial(5*n-k,n-2*k).
Original entry on oeis.org
1, 5, 46, 469, 5017, 55177, 617905, 7008264, 80241790, 925457822, 10735707149, 125128265025, 1464140655619, 17188834766497, 202366206841241, 2388313959181973, 28246993739096305, 334711010978735163, 3972765235517468758, 47224110710958716845
Offset: 0
A371785
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-k,n-2*k).
Original entry on oeis.org
1, 3, 14, 76, 441, 2652, 16303, 101727, 641630, 4080154, 26112384, 167978615, 1085182436, 7035477777, 45750406205, 298279844724, 1949096816505, 12761551428024, 83701819019155, 549850618355886, 3617119500327536, 23824816811652905, 157106267803712709
Offset: 0
Showing 1-4 of 4 results.