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 A276696 Triangle read by rows, T(n,k) = T(n-1, k-1) + T(n-2, k) if k is odd, T(n-1, k-1) + T(n-1, k) if k is even, for k<=0<=n and n>=2 with T(0,0)=T(1,0)=T(1,1)=0 and T(n,k)=0 when k>n, k<0, or n<0. 0
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 5, 3, 1, 1, 3, 9, 8, 8, 3, 1, 1, 4, 12, 14, 16, 9, 4, 1, 1, 4, 16, 20, 30, 19, 13, 4, 1, 1, 5, 20, 30, 50, 39, 32, 14, 5, 1, 1, 5, 25, 40, 80, 69, 71, 36, 19, 5, 1, 1, 6, 30, 55, 120, 119, 140, 85, 55, 20, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS This is the triangle frst(n,k) in the Ehrenborg and Readdy link. See Definition 3.1 and Table 1. LINKS Richard Ehrenborg, Margaret A. Readdy, The Gaussian coefficient revisited, arXiv:1609.03216 [math.CO], 2016. EXAMPLE Triangle starts: 1; 1, 1; 1, 1, 1; 1, 2, 2, 1; 1, 2, 4, 2, 1; 1, 3, 6, 5, 3, 1; 1, 3, 9, 8, 8, 3, 1; ... MATHEMATICA T[n_, n_] = T[_, 0] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = If[OddQ[k], T[n-1, k-1] + T[n-2, k], T[n-1, k-1] + T[n-1, k]]; T[_, _] = 0; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 28 2018 *) PROG (PARI) frst(n, k) = if ((k>n) || (n<0) || (k<0), 0, if (n<=2, 1, if (k==0, 1, if (k%2, frst(n-1, k-1) + frst(n-2, k), frst(n-1, k-1) + frst(n-1, k))))); tf(nn) = for (n=0, nn, for (k=0, n, print1(frst(n, k), ", "); ); print(); ); CROSSREFS Cf. A169623 (the triangle er). Sequence in context: A199204 A262750 A075402 * A220777 A088855 A034851 Adjacent sequences:  A276693 A276694 A276695 * A276697 A276698 A276699 KEYWORD nonn,tabl AUTHOR Michel Marcus, Sep 14 2016 STATUS approved

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Last modified November 16 00:11 EST 2018. Contains 317252 sequences. (Running on oeis4.)