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 A124642 Antidiagonal sums of A096465. 2
 1, 1, 2, 3, 5, 9, 15, 29, 50, 99, 176, 351, 638, 1275, 2354, 4707, 8789, 17577, 33099, 66197, 125477, 250953, 478193, 956385, 1830271, 3660541, 7030571, 14061141, 27088871, 54177741, 104647631, 209295261, 405187826, 810375651, 1571990936, 3143981871, 6109558586, 12219117171, 23782190486, 47564380971, 92705454896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Apparently bisections give A024718 and A006134 and are related to A078478, A100066 and A105848. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA Conjecture: G.f.: -(1/2)*z*(2*z+(1-4*z^2)^(1/2)+1)/(1-4*z^2)^(1/2)/(z^2-1). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009 From G. C. Greubel, Apr 30 2021: (Start) a(n) = (1 + (-1)^n)/2 + Sum_{j=0..floor((n-1)/2)} Sum_{k=0..j} (n-2*j)*binomial(n -2*k, n-k-j)/(n-2*k). a(n) = Sum_{j=0..floor(n/2)} Sum_{k=0..j} ((n-2*j)/(n-k-j))*binomial(n-2*k, n-k-j). (End) MATHEMATICA a[_, 0]=1; a[n_, n_]=1; a[n_, m_]:= a[n, m] = a[n-1, m] + a[n, m-1]; a[n_, m_] /; n<0 || m>n = 0; Table[ Sum[a[n-m, m], {m, 0, n}], {n, 0, 45}] (* Jean-François Alcover, Dec 17 2012 *) a[n_]:= a[n]= (1+(-1)^n)/2 + Sum[(n-2*j)*Binomial[n-2*k, n-k-j]/(n-2*k), {j, 0, (n-1)/2}, {k, 0, j}]; Table[a[n], {n, 0, 45}] (* G. C. Greubel, Apr 30 2021 *) PROG (Magma) a:= func< n | n eq 0 select 1 else (1+(-1)^n)/2 + (&+[ (&+[ ((n-2*j)/(n-2*k))*Binomial(n-2*k, n-k-j) : k in [0..j]]) : j in [0..Floor((n-1)/2)]]) >; [a(n): n in [0..45]]; // G. C. Greubel, Apr 30 2021 (Sage) def a(n): return (1+(-1)^n)/2 + sum( sum( ((n-2*j)/(n-2*k))*binomial(n-2*k, n-k-j) for k in (0..j)) for j in (0..(n-1)//2)) [a(n) for n in (0..45)] # G. C. Greubel, Apr 30 2021 CROSSREFS Cf. A006134, A024718, A078478, A100066, A105848. Sequence in context: A351359 A191701 A066726 * A269153 A232866 A011826 Adjacent sequences: A124639 A124640 A124641 * A124643 A124644 A124645 KEYWORD nonn AUTHOR Gerald McGarvey, Dec 21 2006 EXTENSIONS Offset changed by Reinhard Zumkeller, Jul 12 2012 Terms a(18) onward added by G. C. Greubel, Apr 30 2021 STATUS approved

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Last modified March 26 09:11 EDT 2023. Contains 361529 sequences. (Running on oeis4.)