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 A026756 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747. 10
 1, 3, 8, 18, 42, 90, 204, 432, 972, 2052, 4610, 9726, 21859, 46125, 103783, 219099, 493699, 1042899, 2353716, 4975350, 11247138, 23790714, 53867343, 114020601, 258571256, 547672566, 1243848888, 2636201532, 5995717860 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 MAPLE A026747 := proc(n, k) option remember;    if n<0 then 0;    elif k=0 or k = n then 1;    elif type(n, 'even') and k <= n/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(add(add(A026747(i, j), j=0..n), i=0..n), n=0..30); # G. C. Greubel, Oct 29 2019 MATHEMATICA T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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[i, j], {i, 0, n}, {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Oct 29 2019 *) PROG (Sage) @CachedFunction def T(n, k):     if (n<0): return 0     elif (k==0 or k==n): return 1     elif (mod(n, 2)==0 and k<=n/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(sum(T(i, j) for j in (0..n)) for i in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 29 2019 CROSSREFS Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026757. Sequence in context: A066425 A026679 A191524 * A341583 A216631 A026384 Adjacent sequences:  A026753 A026754 A026755 * A026757 A026758 A026759 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)