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 A027218 a(n) = Sum_{k=0..n-3} T(n,k)*T(n,k+3), T given by A026736. 1
 1, 9, 51, 279, 1277, 6235, 26789, 125370, 525082, 2409886, 9969722, 45289767, 186105280, 840402559, 3439358196, 15472942142, 63155131233, 283400162019 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS G. C. Greubel, Table of n, a(n) for n = 3..1000 MATHEMATICA T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/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[Sum[T[n, k]*T[n, k+3], {k, 0, n-3}], {n, 3, 30}] (* G. C. Greubel, Jul 19 2019 *) PROG (PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/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=3, 20, print1(sum(k=0, n-3, T(n, k)*T(n, k+3)), ", ")) \\ G. C. Greubel, Jul 19 2019 (Sage) @CachedFunction def T(n, k): if (k==0 or k==n): return 1 elif (mod(n, 2)==0 and k==(n-2)/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) [sum(T(n, k)*T(n, k+3) for k in (0..n-3)) for n in (3..30)] # G. C. Greubel, Jul 19 2019 (GAP) T:= function(n, k) if k=0 or k=n then return 1; elif k=n-1 then return n; elif (n mod 2)=0 and k=Int((n-2)/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; List([3..20], n-> Sum([0..n-3], k-> T(n, k)*T(n, k+3) )); # G. C. Greubel, Jul 19 2019 CROSSREFS Cf. A026736. Sequence in context: A080624 A125319 A080621 * A155617 A126477 A275861 Adjacent sequences: A027215 A027216 A027217 * A027219 A027220 A027221 KEYWORD nonn AUTHOR Clark Kimberling STATUS approved

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Last modified September 8 19:26 EDT 2024. Contains 375754 sequences. (Running on oeis4.)