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 A026634 a(n) = Sum_{k=0..floor(n/2)} A026626(n, k). 16
 1, 1, 4, 5, 15, 22, 59, 90, 230, 362, 902, 1450, 3551, 5802, 14022, 23210, 55492, 92842, 219974, 371370, 873101, 1485482, 3468893, 5941930, 13793183, 23767722, 54880915, 95070890, 218480607, 380283562, 870164852, 1521134250 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = floor(A026633(n)/2) if (n mod 2) = 1 and a(n) = floor((2*A026633(n) + (1+(-1)^n)*A026627(floor(n/2)+1))/4) if (n mod 2) = 0. - G. C. Greubel, Jun 21 2024 MATHEMATICA T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, (6*n-1 + (-1)^n)/4, T[n-1, k-1] +T[n-1, k]]]; A026634[n_]:= Sum[T[n, k], {k, 0, n}]; Table[A026634[n], {n, 0, 40}] (* G. C. Greubel, Jun 21 2024 *) PROG (Magma) b:= func< n | n le 2 select 2*n-1 else ((357*n^3-2696*n^2+6441*n-4822)*Self(n-1) +2*(2*n-7)*(51*n^2-203*n+188)*Self(n-2))/(2*(n-1)*(51*n^2-305*n+442)) >; A026627:= [b(n+1) : n in [0..60]]; A026633:= [n le 1 select n+1 else (17*2^(n-2) +(-1)^n)/3 -1: n in [0..60]]; function A026634(n) if (n mod 2) eq 1 then return Floor(A026633[n+1]/2); else return Floor( (2*A026633[n+1] + (1+(-1)^n)*A026627[Floor(n/2) +1])/4); end if; end function; [A026634(n): n in [0..60]]; // G. C. Greubel, Jun 21 2024 (SageMath) @CachedFunction def T(n, k): # T = A026626 if (k==0 or k==n): return 1 elif (k==1 or k==n-1): return int(3*n//2) else: return T(n-1, k-1) + T(n-1, k) def A026634(n): return sum(T(n, k) for k in range((n//2)+1)) [A026634(n) for n in range(41)] # G. C. Greubel, Jun 21 2024 CROSSREFS Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632. Cf. A026633, A026635, A026636, A026961, A026962, A026963, A026964. Cf. A026965. Sequence in context: A267991 A225536 A084179 * A026656 A184244 A006491 Adjacent sequences: A026631 A026632 A026633 * A026635 A026636 A026637 KEYWORD nonn AUTHOR Clark Kimberling STATUS approved

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Last modified September 11 21:59 EDT 2024. Contains 375839 sequences. (Running on oeis4.)