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 A027221 Sum of squares of numbers in row n of array T given by A026736. 1
 1, 2, 6, 20, 79, 284, 1237, 4542, 20626, 76406, 354080, 1317964, 6173634, 23051344, 108628550, 406513364, 1922354351, 7206349304, 34147706833, 128187589014, 608151037123, 2285559568866, 10850577045131, 40817923301712, 193850277807569, 729825857819924, 3466587141136257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..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]^2, {k, 0, n}], {n, 0, 40}] (* 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) )); vector(21, n, n--; sum(k=0, n, T(n, k)^2 ) ) \\ 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)^2 for k in (0..n)) for n in (0..40)] # 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([0..21], n-> Sum([0..n], k-> T(n, k)^2 )); # G. C. Greubel, Jul 19 2019 CROSSREFS Cf. A026736. Sequence in context: A081563 A038393 A357798 * A346747 A300514 A150183 Adjacent sequences: A027218 A027219 A027220 * A027222 A027223 A027224 KEYWORD nonn AUTHOR Clark Kimberling STATUS approved

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Last modified August 10 12:12 EDT 2024. Contains 375056 sequences. (Running on oeis4.)