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%I M2779 M2780 #48 Jan 31 2022 01:33:23
%S 1,3,9,21,51,117,271,607,1363,3013,6643,14491,31495,67965,146115,
%T 312483,666015,1413915,2992815,6315135,13292007,27906585,58464339,
%U 122229123,255072423,531369483,1105217223,2295383319,4760727375
%N Number of weighted voting procedures.
%D M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 122-123.
%D T. V. Narayana, Recent progress and unsolved problems in dominance theory, pp. 68-78 of Combinatorial mathematics (Canberra 1977), Lect. Notes Math. Vol. 686, 1978.
%D T. V. Narayana, Lattice Path Combinatorics with Statistical Applications. Univ. Toronto Press, 1979, pp. 100-101.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Solution to Board of Directors Problem, J. Rec. Math., 9 (No. 3, 1977), 240.
%H Reinhard Zumkeller, <a href="/A005254/b005254.txt">Table of n, a(n) for n = 1..1000</a>
%H G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1983__84__45_0">Sur quelques problèmes relatifs au vote pondéré</a>, [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.
%H B. E. Wynne & N. J. A. Sloane, <a href="/A002083/a002083_1.pdf">Correspondence, 1976-84</a>
%H B. E. Wynne & T. V. Narayana, <a href="/A002083/a002083_2.pdf">Tournament configuration, weighted voting, and partitioned catalans</a>, Preprint.
%H Bayard Edmund Wynne, and T. V. Narayana, <a href="http://www.numdam.org/item?id=BURO_1981__36__75_0">Tournament configuration and weighted voting</a>, Cahiers du bureau universitaire de recherche opérationnelle, 36 (1981): 75-78.
%H <a href="/A005254/a005254.pdf">Solution to Board of Directors Problem</a>, J. Rec. Math., 9 (No. 3, 1977), 240. (Annotated scanned copy)
%t a[1, 1] = 1; a[n_, 1] := a[n, 1] = a[n - 1, Floor[(n + 1)/2]]; a[n_, k_ /; k > 1] := a[n, k] = a[n, 1] + a[n - 1, k - 1]; A005254 = Table[ Sum[ a[n, k], {k, 1, n}], {n, 1, 29}] (* _Jean-François Alcover_, Apr 03 2012, after recurrence of A037254 *)
%o (Haskell)
%o a005254 = sum . a037254_row -- _Reinhard Zumkeller_, Nov 18 2012
%Y Row sums of A037254.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Feb 04 2000
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